Question

If $\sqrt{1-\cos x}=\sin x$, then $x$ is equal to , where $nϵI$

• A. $(2n+1)\frac{\pi }{2}$
• B. $2n\pi +\pi /4$ or $n\pi$
• C. $n\pi$ or $(2n+1)\frac{\pi }{4}$
• D. $noneofthese$

Answer 1

Answer: (A)

$(2n+1)\frac{\pi }{2}$

Given $\sqrt{1-\cos x}=\sin x$

Squaring on both sides

$1-\cos x={\sin }^{2}x$

$⟹1-\cos x=1-{\cos }^{2}x$

$⟹(1-\cos x)=(1-\cos x)(1+\cos x)$

So $\cos x=0$ or $\cos x=1$

$⟹x=(2n+1)\frac{\pi }{2}$ or $2n\pi$