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

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

Quizplus · Accepted Answer

Using the sum angle formulas for cosine and sine, we have:

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

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

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