Guysss i need help

**^_^Engineer_Adam^_^** · August 20th 2006, 04:12 AM

Verify:
sin( pie / 2 - x) = cos x

**CaptainBlack** · August 20th 2006, 05:45 AM

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

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