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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Exercise MCQs Question 12 Maths Textbook Solution.

Provide Solution For R.D.Sharma Maths Class 12 Chapter 3 Inverse Trigonometric Functions Exercise MCQs Question 12 Maths Textbook Solution.

Answers (1)

Answer: \sqrt{\tan \theta}

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

Given: u=\cot ^{-1} \sqrt{\tan \theta}-\tan ^{-1} \sqrt{\tan \theta}

Solution:

            y=\sqrt{\tan \theta}

Then, u=\cot ^{-1} \sqrt{\tan \theta}-\tan ^{-1} \sqrt{\tan \theta}

         \begin{aligned} &=\cot ^{-1} y-\tan ^{-1} y \\ &u=\frac{\pi}{2}-2 \tan ^{-1} y \\ &2 \tan ^{-1} y=\frac{\pi}{2}-u \\ &\tan ^{-1} y=\frac{\pi}{4}-\frac{u}{2} \\ &y=\tan \left(\frac{\pi}{4}-\frac{u}{2}\right) \\ &\sqrt{\tan \theta}=\tan \left(\frac{\pi}{4}-\frac{u}{2}\right) \\ &\therefore y=\sqrt{\tan \theta} \end{aligned}

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