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  • Explain Solution R.D Sharma Class 12 Chapter 10 Differentiation Exercise 10.3 Question 37 Sub Question 1 Maths Textbook Solution.

Explain Solution R.D Sharma Class 12 Chapter 10  Differentiation  Exercise 10.3 Question 37 Sub Question 1 Maths Textbook Solution.

Answers (1)

Answer: \frac{dy}{dx}=-1

Hint:

\begin{aligned} &\frac{\mathrm{d}}{\mathrm{dx}}(\text { constan } \mathrm{t})=0 \\ &\frac{d}{d \mathrm{x}}\left(\mathrm{x}^{\mathrm{n}}\right)=\mathrm{n} \mathrm{x}^{\mathrm{n}-1} \end{aligned}

Given:

\cos ^{-1}\left ( \sin x \right )

Solution:

Let,

y=\cos ^{-1}\left ( \sin x \right )

We observe that this function is defined for all real numbers

\begin{aligned} &y=\cos ^{-1}(\sin x) \\ &y=\cos ^{-1}\left[\cos \left(\frac{\pi}{2}-x\right)\right] \\ &y=\frac{\pi}{2}-x \end{aligned}                                                                        \left\{\begin{array}{r} \operatorname{since} \cos ^{-1}(\cos \theta)=\theta \\ \text { if } \theta \in[\theta, \mathbf{\pi}] \end{array}\right\}

Differentiating it with respect to x,

\begin{aligned} &\frac{d y}{d x}=0-1 \\ &\frac{d y}{d x}=-1 \end{aligned}                                                                                                            \left \{ Since,\frac{d\left ( constant \right )}{dx}=0 \right \}

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