1-cos(pi+x)-sin (3pi+x/2)=0

Question

1-cos(pi+x)-sin (3pi+x/2)=0

Answer 1

1-сos(π+x)-sin(3π+x/2)=0
1+cosx+cosx/2=0
1+2cos²x/2-1+cosx/2=0
2cos²x/2+cosx/2=0
cosx/2*(2cosx/2+1)=0
cosx/2=0⇒x/2=π/2+πn⇒x=π+2πn
cosx/2=-1/2⇒x/2=+-2π/3+2πn⇒x=+-4π/3+4πn