Notes: Show that sin(pi/2-x)=cosx?

Friday, June 3, 2011

Show that sin(pi/2-x)=cosx?

We'll have to apply the following identity to prove the
given expression:

sin(a-b) = sin a*cos b - sin b*cos
a

Let a = $\displaystyle\pi$ /2 and b =
x

sin ( $\displaystyle\pi$ /2 - x) = sin $\displaystyle\pi$ /2*cos x - sin x* cos $\displaystyle\pi$
/2

But sin $\displaystyle\pi$ /2 = 1 and cos $\displaystyle\pi$ /2 =
0

sin ( $\displaystyle\pi$ /2 - x) = 1*cos x - sin
x*0

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

Therefore, the given expression sin ( $\displaystyle\pi$
/2 - x) = cos x represents an identity.

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