Verify cos(x-3pi/2)=-sin x

Answer 1

3 pi / 2 = 270 °

sin ( 3 pi / 2 ) = sin 270 ° = - 1

cos ( 3 pi / 2 ) = cos 270 ° = 0

cos ( A - B ) = cos A cos B + sin A sin B

In this case :

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

cos ( x ) * 0 + sin ( x ) * ( - 1 ) =

0 - sin ( x ) = - sin ( x )