Question

If ${\displaystyle y=\frac{\sin (x+9)}{\cos x}}$ then ${\displaystyle \frac{dy}{dx}}$ at x = 0 is ______.

विकल्प

• cos 9

• sin 9

• 0

• 1

Answer 1

If ${\displaystyle y=\frac{\sin (x+9)}{\cos x}}$ then ${\displaystyle \frac{dy}{dx}}$ at x = 0 is cos 9.

Explanation:

Given ${\displaystyle y=\frac{\sin (x+9)}{\cos x}}$

${\displaystyle \frac{dy}{dx}=\frac{\cos x\cdot \cos (x+9)-\sin (x+9)(-\sin x)}{{\cos }^{2}x}}$

= ${\displaystyle \frac{\cos x\cos (x+9)+\sin x\sin (x+9)}{{\cos }^x}}$

= ${\displaystyle \frac{\cos (x+9-x)}{{\cos }^{2}x}}$

= ${\displaystyle \frac{\cos 9}{{\cos }^{2}x}}$

∴ ${\displaystyle {\left(\frac{dy}{dx}\right)}_{\text{at} x=0}=\frac{\cos 9}{{\cos }^{2}0}}$

= ${\displaystyle \frac{\cos 9}{{\left(1\right)}^2}}$

= cos 9