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Verified Answer :

MathisLif3

cos (x+pi/2)=-sinx
sin (pi+x)=-sinx
=-2sinx

wizard123

To completely show how this can be simplified to -2sin(x), use angle sum formulas for sin/cos.
\(cos (a+b) = cos (a) cos (b) - sin (a) sin (b) \\ sin(a+b) = sin (a) cos (b) + sin (b) cos (a)\)

Apply to given problem:
\(=cos (x) cos (\frac{\pi}{2}) - sin (x) sin (\frac{\pi}{2}) +sin (x) cos (\pi) + sin (\pi) cos (x) \\= 0-sin(x) -sin(x)+0 \\ = -2 sin (x)\)

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