Question

Solve : $\left(\tan y\right)\frac{dy}{dx}=\sin (x+y)+\sin (x-y)$

• A. $\sec y=-2\cos x+C$
• B. $\sec y=2\cos x+C$
• C. $\sec y=-\cos x+C$
• D. $\sec y=\cos x+C$

Answer 1

The correct option is A $\sec y=-2\cos x+C$

Given, $\left(\tan y\right)\frac{dy}{dx}=\sin (x+y)+\sin (x-y)=2\sin x\cos y$

$\Rightarrow \left(\sec y\tan y\right)dy=\sin xdx$

$\Rightarrow d\left(\sec y\right)=-2d\left(\cos x\right)$

Integrating on both sides we get,

$\sec y=-2\cos x+c$