Content of this article has been merged with Chapter 2 Inverse Trigonometric Functions – Miscellaneous Exercise as per the revised syllabus of NCERT.
Question 11. Prove
Solution:
Put
so that, Then, we have :
LHS =
=
=
=
=
–
L.H.S = R.H.S
Hence Proved
Question 12. Prove
Solution:
L.H.S. =
=
Using
=
-(1) Now, let
Then,
Using equation(1), we get,
=
L.H.S = R.H.S
Hence Proved
Question 13. Solve
Solution:
=
– =
=
= cos x/sin x
= cot x =1
Therefore, x = π/4
Question 14. Solve
Solution:
Let x = tanθ
π/4 – θ = θ/2
θ = π/6
So, x = tan(π/6) = 1/√3
Question 15. Solve is equal to
(A) (B) (C) (D)
Solution:
Let tan y = x,
Let
Then,
So, the correct answer is D.
Question 16. Solve , then x is equal to
(A) 0, 1/2 (B) 1, 1/2 (C) 0 (D) 1/2
Solution:
-(1) Let
Therefore, from equation(1), we have
Put x = siny then, we have:
sin y = 0 or 1/2
x = 0 or x = 1/2
But, when x = 1/2 it can be observed that:
L.H.S. =
=
=
=
x = 1/2 is not the solution of given equation.
Thus, x = 0
Hence, the correct answer is C
Question 17. Solve is equal to
(A) π/2 (B) π/3 (C) π/4 (D) -3π/4
Solution
–
Hence, the correct answer is C