Question

if $x=\frac{\pi }{2},$ satisfies the equation $\sin \frac{nx}{2}-\cos \frac{nx}{2}=1-\sin nx$ & the inequality $|\frac{nx}{2}-\frac{\pi }{2}|\le \frac{3\pi }{4},$ then

• A. $n=-1,0,3,5$
• B. $n=1,2,4,5$
• C. $n=1,2,4$
• D. $n=-1,1,3,5$

Answer 1

The correct option is C $n=1,2,4$

$n=1,2,4,5,\mathrm{6...}$ satisfies the equation $\sin \frac{nx}{2}-\cos \frac{nx}{2}=1-\sin x$

but

$|\frac{nx}{2}-\frac{\pi }{2}|\le \frac{3\pi }{4}$ is only satisfied when $n=1,2,4$

Therefore, Answer is $n=1,2,4$