Question

If ${\int }_{\pi /3}^x\sqrt{(3-{\sin }^{2}z)dz}+{\int }_0^y\cos zdz=0$

then $\frac{dy}{dx}$ equals?

• A. $\frac{\sqrt{{\sin }^{2}x-3}}{\cos y}$
• B. $\frac{\cos y}{\sqrt{3-{\sin }^{2}x}}$
• C. $\frac{\sqrt{3-{\sin }^{2}x}}{\cos y}$
• D. $-\frac{\sqrt{3-{\sin }^{2}x}}{\cos y}$

Answer 1

Answer: (D)

$-\frac{\sqrt{3-{\sin }^{2}x}}{\cos y}$

${\int }_{\pi /3}^x\sqrt{(3-{\sin }^{2}z)dz}+{\int }_0^y\cos zdz=0$
Differentiating this we get
$\sqrt{(3-{\sin }^{2}x)}dx+\cos ydy=0$
$\Rightarrow \frac{dy}{dx}=-\frac{(3-{\sin }^{2}x)}{\cos y}$