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  • Please solve RD Sharma class 12 chapter 10 Differentiation exercise Multiple choice question 30 maths textbook solution

Please solve RD Sharma class 12 chapter 10 Differentiation exercise Multiple choice question 30 maths textbook solution

Answers (1)

Answer:

        \frac{\cos ^{2}(a+y)}{\cos a}

Hint:

     Differentiate the function w.r.t x    

Given:

        \sin y=x \cos (a+y)

Solution:  

        \begin{aligned} &\sin y=x \cos (a+y) \\\\ &\frac{d}{d x}(\sin y)=\frac{d}{d x}[x \cos (a+y)] \end{aligned}

        \begin{aligned} &\cos y \frac{d y}{d x}=1 \times \cos (a+y)-x \sin (a+y) \frac{d}{d x}(a+y) \\\\ &\cos y \frac{d y}{d x}=\cos (a+y)-x \sin (a+y) \frac{d y}{d x} \end{aligned}

        \begin{aligned} &\cos y \frac{d y}{d x}+x \sin (a+y) \frac{d y}{d x}=\cos (a+y) \\\\ &{[\cos y+x \sin (a+y)] \frac{d y}{d x}=\cos (a+y)} \end{aligned}

        \left[\cos y+\frac{\sin y}{\cos (a+y)} \times \sin (a+y)\right] \frac{d y}{d x}=\cos (a+y)        \left[\begin{array}{l} \sin y=x \cos (a+y) \\\\ x=\frac{\sin y}{\cos (a+y)} \end{array}\right]

        \left[\frac{\cos (a+y) \cos y+\sin y \sin (a+y)}{\cos (a+y)}\right] \frac{d y}{d x}=\cos (a+y)

        \begin{aligned} &\frac{\cos (a+y-y)}{\cos (a+y)} \times \frac{d y}{d x}=\cos (a+y) \\\\ &\frac{d y}{d x}=\frac{\cos ^{2}(a+y)}{\cos a} \end{aligned}

 

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