How do I prove the following identities?
sin(3pi/2 + x) = -cos x
sin(pi/2+h)-sin(pi/2) ...cos h-1
_________________ = ______
............h ....................h
Please help I am having alot of trouble with these? Thanks
How do I prove the following identities?
sin(3pi/2 + x) = -cos x
sin(pi/2+h)-sin(pi/2) ...cos h-1
_________________ = ______
............h ....................h
Please help I am having alot of trouble with these? Thanks
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