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

Name: $\cos \left( x + \frac { \pi } { 2 } \right) + \sin \left( x + \frac { \pi } { 2 } \right) = \cos x - \sin x$
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Question

Quizplus · Accepted Answer

The left-hand side of the equation can be rewritten as $\cos x \cos \frac{\pi}{2} + \sin x \sin \frac{\pi}{2} = \cos x (0) + \sin x (1) = \sin x$. The right-hand side of the equation is $\cos x - \sin x$. Therefore, the equation is true.

cos⁡(x+π2)+sin⁡(x+π2)=cos⁡x−sin⁡x\cos \left( x + \frac { \pi } { 2 } \right) + \sin \left( x + \frac { \pi } { 2 } \right) = \cos x - \sin xcos(x+2π​)+sin(x+2π​)=cosx−sinx

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