Question

A value of x satisfying the equation sin[cot⁻¹(1 + x)] = cos[tan⁻¹x] is

(A) 1/2

(B) 0

(C) –1

(D) - 1/2

Answer 1

Correct option (A) 1/2

Explanation:

We have the following two cases:

Therefore, the value of x satisfying the given equation is found as follows:

sin[cot^-1(1 + x)] = cos[tan^-1(x)]

= x² + 2x + 2 = 1 + x²

That is, 2x = - 1 ⇒ x = - 1/2