Question

Cos(x+(pi/2))+sin(pi+x)
Simplified is?

Answer 1

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 ((\pi)/(2)) - sin (x) sin ((\pi)/(2)) +sin (x) cos (\pi) + sin (\pi) cos (x) \\= 0-sin(x) -sin(x)+0 \\ = -2 sin (x)`

Answer 2

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