Question

Solution of the equation $cosy=cosx$

• A. $y=n\pi +(-1{)}^{n}x$
• B. $y=2n\pi +x$
• C. $n\pi +x$
• D. $n\pi +x$

Answer 1

The correct option is B

$y=2n\pi +x$

$cosy=cosx$

$cosx-cosy=0$

$2sin\frac{(y+x)}{2}.sin\frac{(y-x)}{2}=0$

$sin\frac{(x+y)}{2}=0orsin\frac{(y-x)}{2}=0$

$\frac{x+y}{2}=n\pi$ or $\frac{y-x}{2}=n\pi$

$x+y=2n\pi$ or $y-x=2n\pi$

or $y=2n\pi$ - x or $y=2n\pi +x$

so,$y=2n\pi +x$ is the correct answer from options