Question

The value of sin cot^–1 (tan (cos^–1 x)) is equal to-

• A. x
• B. $\frac{\pi}{2}$
• C. 1
• D. None of these

Answer 1

Answer: (A)

x

Answer 2

Let cos^–1 x = q ̃ x = cos q ̃ sec q = 1/x

̃ tan q = $\sqrt{\sec^{2}\theta - 1}$= 1/x $\sqrt{1 - x^{2}}$

Now sin cot^–1 tan q = sincot^–1($1/x\sqrt{1 - x^{2}}$)

put x = sin q sin cot^–1($1/x\sqrt{1 - x^{2}}$)

= sin cot^–1[$\sqrt{1 - \sin^{2}\theta}/\sin\theta$]

= sin cot^–1 (cot q) = sin q = x