Question

If a $co{s}^2(x+y)=b$, then $\frac{dy}{dx}$ equals

• A. 2
• B. -2
• C. 1
• D. -1

Answer 1

The correct option is D -1

Differentiating both sides w.r.t $x$

$2a\cos (x+y).(-\sin (x+y\left)\right)[1+\frac{dy}{dx}]=0$

$-a\sin (2x+2y)[1+\frac{dy}{dx}]=0$

$x+y=\frac{n\pi }{2}$ or $\frac{dy}{dx}+1=0$

In Both cases $\frac{dy}{dx}=-1$