Question

Cos x/4*sin pi/5-sin x/4*cos pi/5=√2/2

Answer 1

$cos \frac{x}{4} sin \frac{ \pi }{5} -sin \frac{x}{4} cos \frac{ \pi }{5} = \frac{ \sqrt{2} }{2}$

$sin( \frac{x}{4}- \frac{ \pi }{5} )= \frac{ \sqrt{2} }{2}$

$\frac{x}{4} + \frac{ \pi }{5} =(-1) ^{k} \frac{ \pi }{4}+ \pi k,$ k∈Z

$\frac{x}{4} =(-1) ^{k} \frac{ \pi }{20} + \pi k,$ k∈Z

$x=(-1) ^{k} \frac{ \pi }{5} + \pi k,$ k∈Z