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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 10 Differentiation Exercise 10.3 Question 12 Sub Question 2 Maths Textbook Solution.

Provide Solution For R.D.Sharma Maths Class 12 Chapter 10 Differentiation Exercise 10.3  Question 12 Sub Question 2 Maths Textbook Solution.

Answers (1)

Answer:

\frac{dy}{dx}=\frac{1}{2}

Hint:

\cos 2x=2\cos ^{2}x-1

\tan \left ( \frac{\pi }{2} -\theta \right )=\cot \theta

Given:

\tan ^{-1}\left \{ \frac{1+\cos x}{sinx} \right \}

Solution:

\begin{aligned} &y=\tan ^{-1}\left\{\frac{1+\cos x}{\sin x}\right\} \\ &y=\tan ^{-1}\left\{\frac{2 \cos ^{2} \frac{x}{2}}{2 \sin \frac{x}{2} \cos \frac{x}{2}}\right\} \\ &y=\tan ^{-1}\left(\cot \frac{x}{2}\right) \\ &y=\tan ^{-1}\left(\tan \left(\frac{\pi}{2}-\frac{x}{2}\right)\right) \end{aligned}                                \left [ \left ( \frac{\pi }{2} -\theta \right )=\cot \theta \right ]

y=\frac{x}{2}

Differentiating w.r.t x

\frac{dy}{dx}=\frac{1}{2}

Solution:

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