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  • Choose the correct answer out of 4 options given against each Question If y=sin⁡(x+9)/cos⁡x at x = 0 is A. cos 9

Choose the correct answer out of 4 options given against each Question

If y=\frac{\sin \left( x+9 \right) }{\cos x} then \frac{d y}{d x} \text { at } x=0   is 

A. cos 9
B. sin 9
C. 0
D. 1

Answers (1)

\\ y=\frac{\sin \left( x+9 \right) }{\cos x} \\ \\ \frac{dy}{dx}=\frac{\cos x\cos \left( x+9 \right) -\sin \left( x+9 \right) \left( -\sin x \right) }{\cos ^{2}x} \\ \\ =\frac{\cos x\cos \left( x+9 \right) +\sin \left( x+9 \right) \sin x}{\cos ^{2}x} \\ \\ =\frac{\cos \left( x+9-x \right) }{\cos ^{2}x}=\frac{\cos 9}{\cos ^{2}x} \\ \\ \left( \frac{dy}{dx} \right) _{x=0}=\frac{\cos 9}{ \left( 1 \right) ^{2}}=\cos 9 \\ \\

Hence, the answer is option A

Posted by

infoexpert21

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