How do you solve $sin (x- (pi/2))= cos x$ ?

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Answer 1 · 2016-01-27T08:45:14

$x=pi/2$

$sin A=cos (pi/2-A)$

Therefore, from the given equation

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

If $A=x-pi/2$ , then

$sin (x-pi/2)=cos (pi/2-(x-pi/2))$ it follows that

$cos x=cos (pi/2-(x-pi/2))$

Equate the angles now

$x=pi/2-(x-pi/2))$

$x=pi/2-x+pi/2$

$x+x=pi/2+pi/2$

$2x=pi$

$x=pi/2$

Check using the original equation:

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

$sin (pi/2-pi/2)=cos (pi/2)$

$sin 0=cos (pi/2)$

$0=0$

correct, therefore $x=pi/2$

How do you solve sin (x- (pi/2))= cos x sin (x- (pi/2))= cos x?