Решить уравнение.

sin (p+4x) - sin (3p/2-4x) = 0

Sin (π+4x) - sin (3π/2-4x) = 0

-sin4x+cos4x=0

-2sin2xcos2x+cos²2x-sin²2x=0/cos²2x

tg²2x+2tg2x-1=0

tg2x=a

a²+2a-1=0

D=4+4=8

a1 = (-2-2√2) / 2=-1-√2⇒tg2x=-1-√2⇒2x=-arctg (1+√2) + πn⇒

x=-1/2arctg (1+√2) + πn/2, n∈z

a2=-1+√2⇒tg2x=√2-1⇒2x=arctg (√2-1) + πn⇒x=1/2arctg (√2-1) + πn/2, n∈z