How do you verify $cos (\frac{π}{2} - x) cos x = cos x$ $cos (pi/2 -x) cos x = cos x$ ?

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Answer 1 · 2016-04-16T23:38:56

See below

LHS =left hand side, RHS =right hand side

Use formula $cos (A - B) = cos A cos B + sin A sin B$ $cos(A-B)=cos A cos B + sin A sin B$

$= [cos (\frac{π}{2}) cos x + sin (\frac{π}{2}) sin x] cos x$ $=[cos (pi/2) cosx+sin (pi/2)sinx ]cosx$

$= [0 \times cos x + 1 \times sin x] cos x$ $=[0 xx cosx +1 xx sinx]cosx$

$= sin x cos x$ $=sinx cosx$

Not cos x

How do you verify cos (pi/2 -x) cos x = cos xcos(π2−x)cosx=cosxcos (pi/2 -x) cos x = cos x?