# Guysss i need help

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• Aug 20th 2006, 05:12 AM
^_^Engineer_Adam^_^
Guysss i need help
Verify:
sin( pie / 2 - x) = cos x
• Aug 20th 2006, 06:45 AM
CaptainBlack
Quote:

Originally Posted by ^_^Engineer_Adam^_^
Verify:
sin( pie / 2 - x) = cos x

The summation identity is:

$\sin(A+B)=\sin(A) \cos(B)+\cos(A) \sin(B)$.

Put $A=\pi/2$, and $B=-x$ giving:

$\sin(\pi/2-x)=\sin(\pi/2) \cos(-x)+\cos(\pi/2) \sin(-x)$,

but $\sin(\pi/2)=1$, and $\cos(\pi/2)=0$, so:

$\sin(\pi/2+x)= \cos(-x)$.

However $\cos$ is an even function so $\cos(-x)=\cos(x)$, hence:

$\sin(\pi/2+x)= \cos(x)$.

RonL