cheychey87 Posts: 1, Reputation: 1 New Member #1 Mar 24, 2011, 10:18 PM
prove that cos((pi/2-x)-y)=sin(x y)?
Help help trig trig help
 ebaines Posts: 12,132, Reputation: 1307 Expert #2 Mar 25, 2011, 07:37 AM

Please note that for some reason this site loses any "+" signs that you put in the subject header for your question. I assume what you mean is this:

$
\cos((\frac {\pi} 2 -x)-y) = \sin(x+y)
$

This is a siimple use of the identities for $\cos (a-b)$ and $\sin (a+b)$, and also use of $\cos (\frac {\pi} 2 - x) = \sin x$ and $\sin(\frac {\pi} 2 - x) = \cos x$.

Alternatively if you recognize that $\cos((\frac {\pi} 2 -x)-y) = \cos(\frac {\pi} 2 -(x+y))$ and apply the identity for $\cos (a-b)$ then it comes right out.

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