I am solving double integral $$ \int_0^{\pi} dx \int_{\pi/2}^{\pi} cos(2x+y)dy. $$ I am not understanding how is the -sin(2x+pi/2) = -cos(2x) and sin(2x+pi) = I am aware that sin(pi/2) = 1 rest is unclear to me.
$\endgroup$ 41 Answer
$\begingroup$One has $$ \sin\left(a+\frac{\pi}2\right)=\sin\left(a\right)\cos\left(\frac{\pi}2\right)+\sin\left(\frac{\pi}2\right)\cos\left(a\right)=\sin (a) \cdot 0+1\cdot \cos(a)=\cos (a). $$
$\endgroup$ 3
