Expand, expand.

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

Lefthand side

= sin(3pi/2 +x)

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

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

= -cos(x)

= Righthand side.

Proven.

----------------------

sin(pi/2+h)-sin(pi/2) ...cos h-1

_________________ = ______

............h ....................h

Rewriting that,

[sin(pi/2 +h) -sin(pi/2)] / h = [cos(h) -1] / h

Lefthand Side

= [sin(pi/2 +h) -sin(pi/2)] / h

= [{sin(pi/2)cos(h) +cos(pi/2)sin(h)} -(1)] / h

= [(1)cos(h) +(0)sin(h) -1] / h

= [cos(h) -1] / h

= Righthand Side

Proven