Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Important Questions Class 12

Please refer to Inverse Trigonometric Functions Class 12 Mathematics Important Questions with solutions provided below. These questions and answers have been provided for Class 12 Mathematics based on the latest syllabus and examination guidelines issued by CBSE, NCERT, and KVS. Students should learn these problem solutions as it will help them to gain more marks in examinations. We have provided Important Questions for Class 12 Mathematics for all chapters in your book. These Board exam questions have been designed by expert teachers of Standard 12.

Class 12 Mathematics Important Questions Inverse Trigonometric Functions

Very Short Answer Type Questions

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Inverse Trigonometric Functions Class 12 Mathematics Important Questions

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Inverse Trigonometric Functions Class 12 Mathematics Important Questions

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Inverse Trigonometric Functions Class 12 Mathematics Important Questions

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Inverse Trigonometric Functions Class 12 Mathematics Important Questions

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Inverse Trigonometric Functions Class 12 Mathematics Important Questions

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Inverse Trigonometric Functions Class 12 Mathematics Important Questions

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Inverse Trigonometric Functions Class 12 Mathematics Important Questions

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Inverse Trigonometric Functions Class 12 Mathematics Important Questions

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Inverse Trigonometric Functions Class 12 Mathematics Important Questions

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Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Short Answer Type Questions

Question.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Write the value of the following :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Solve for x:

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Solve for x :
sin−1 (1 – x) – 2 sin−1 x = π/2
Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Solve for x :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

⇒ (x + 6) (x – 1) = 0 ⇒ x = –6, x = 1
But x = – 6 does not satisfy the equation.
∴ x = 1 is the only solution.

Question. Prove that :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Solve for x : cos(2 sin-1x) = 1/9. x > 0
Answer. The given equation is

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove that :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer. Putting x = tan2θ, we get

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Solve for x :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove that: cot–1 7 + cot–1 8 + cot–118 = cot–13.
Answer. L.H.S. = cot–1 7 + cot–1 8 + cot–1 18

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove that :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

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Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove that :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Solve for x :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Prove that :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Find the real solution of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

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Inverse Trigonometric Functions Class 12 Mathematics Important Questions

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Inverse Trigonometric Functions Class 12 Mathematics Important Questions

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Inverse Trigonometric Functions Class 12 Mathematics Important Questions

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Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Long Answer Type Questions

Question. Find the simplified form of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

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Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Write the principal value of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Find the value of the following.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Write the principal value of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Write the principal value of [tan−1(−√3) + tan−1(1)].
Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions
Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Using principal values, write the value of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Find the principal value of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Find the principal value of sec–1(–2).
Answer. Let sec–1(–2) = y. Then, sec y = –2.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Using the principal values, evaluate the following :

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Using principal values, evaluate the following.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer. We know that the range of principal value

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Find the principal value of

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer. We know that, sin–1(sinx) = x

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Find the principal value of tan–1(–1).
Answer. Let tan–1(–1) = x ⇒ –1 = tan x
We know that the range of principal value branch

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. If tan−1 x + tan-1 y = π/4 xy < 1, then write the value of x + y + xy.
Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question. Find the principal value of tan−1√3 −sec−1(−2).
Answer.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Question.

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

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Inverse Trigonometric Functions Class 12 Mathematics Important Questions

CASE STUDY 1:

Inverse Trigonometric Functions Class 12 Mathematics Important Questions

Two men on either side of a temple of 30 meters high observe its top at the angles of elevation 𝛼 and 𝛽 respectively. (as shown in the figure above). The distance between the two men is 40√3 meters and the distance between the first person A and the temple is 30√3 meters. Based on the above information answer the following:


Question. ∠𝐶𝐴𝐵 = 𝛼=
a. sin−1(2/√3)
b. sin−1(1/2)
c. sin−1(2)
d. sin−1(√3/2)

Answer

B

Question. ∠𝐶𝐴𝐵 = 𝛼=
a. cos−1(1/5)
b. cos−1(2/5)
c. cos−1(√3/2)
d. cos−1(4/5)

Answer

C

Question. ∠𝐵𝐶𝐴= 𝛽=
a. tan−1(1/2)
b. tan−1(2)
c. tan−1(1/√3)
d. tan−1(√3)

Answer

D

Question. ∠𝐴𝐵𝐶 =
a. 𝜋/4
b. 𝜋/6
c. 𝜋/2
d. 𝜋/3

Answer

C

Question. Domain and Range of cos−1𝑥=
a. ( −1, 1 ), (0 ,𝜋)
b. [ −1, 1 ], (0 ,𝜋)
c. [ −1, 1 ], [0 ,𝜋]
d. ( −1, 1 ) , [−𝜋/2,𝜋/2]

Answer

C