If y= (x+9) then dy dx at x = 0 is equal to: - Vidyadip

MCQ

If $\text{y}=\frac{\sin(\text{x}+9)}{\cos\text{x}}$ then $\frac{\text{dy}}{\text{dx}}$ at $x = 0$ is equal to:

✓
$\cos9$
B
$\sin9$
C
$0$
D
$1$

✓

Answer

Correct option: A.

$\cos9$

Given $\text{y}=\frac{\sin(\text{x}+9)}{\cos\text{x}}$
$\frac{\text{dy}}{\text{dx}}=\frac{\cos\text{x}.\cos(\text{x}+9)-\sin(\text{x}+9)(-\sin\text{x})}{\cos^{2}\text{x}}$
$=\frac{\cos\text{x}\cos(\text{x}+9)+\sin\text{x}\sin(\text{x}+9)}{\cos^{2}\text{x}}$
$=\frac{\cos(\text{x}+9-\text{x})}{\cos^{2}\text{x}}=\frac{\cos9}{\cos^{2}\text{x}}$
$=\frac{\cos9}{(1)^{2}}$
$=\cos9$

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