JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

1 Easy

1 of 1

Understanding +4 | -1

The value of

\frac{\sin \left(\tan ^{-1} x+\cot ^{-1} x\right)}{\sin \left(\sin ^{-1} x+\cos ^{-1} x\right)}

View answer and explanation

Correct option: A

The correct answer is A (1) because

\tan^{-1}x + \cot^{-1}x = \frac{\pi}{2}

and

\sin^{-1}x + \cos^{-1}x = \frac{\pi}{2}

, so the expression simplifies to

\frac{\sin(\frac{\pi}{2})}{\sin(\frac{\pi}{2})} = 1

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