Question

If ${\sin }^{2}mx+{\cos }^{2}ny=a^{2}then\frac{dy}{dx}$ is equal to

• A. $\frac{m.\sin 2mx}{n.\sin 2ny}$
• B. $\frac{m.\sin mx}{n.\sin nx}$
• C. $\frac{-m.\cos 2mx}{n.\cos 2nx}$
• D. $\frac{n.\sin 2mx}{m.\sin 2nx}$

Answer 1

The correct option is A $\frac{m.\sin 2mx}{n.\sin 2ny}$

$\Rightarrow$${\sin }^{2}mx+{\cos }^{2}ny=a^2$

$\Rightarrow$$2m\sin mx\cos mx-2n\cos ny\sin ny\frac{dy}{dx}=0$

$\Rightarrow$$m\sin 2mx=n\sin 2ny\frac{dy}{dx}$

$\Rightarrow$$\frac{dy}{dx}=\frac{m\sin 2mx}{n\sin 2ny}$