Cos(π/2-x) - sin(-x) + 2sin(π+x) = sin(x) - sin(-x) + 2sin(π+x)
Using trigonometric identities:sin(-x) = -sin(x)sin(π+x) = sin(π)cos(x) + cos(π)sin(x) = 0*cos(x) + (-1)sin(x) = -sin(x)
Therefore:sin(x) - sin(-x) + 2sin(π+x) = sin(x) - (-sin(x)) + 2(-sin(x)) = sin(x) + sin(x) - 2sin(x) = 2sin(x) - 2sin(x) = 0
So, Cos(π/2-x) - sin(-x) + 2sin(π+x) equals 0.
Cos(π/2-x) - sin(-x) + 2sin(π+x) = sin(x) - sin(-x) + 2sin(π+x)
Using trigonometric identities:
sin(-x) = -sin(x)
sin(π+x) = sin(π)cos(x) + cos(π)sin(x) = 0*cos(x) + (-1)sin(x) = -sin(x)
Therefore:
sin(x) - sin(-x) + 2sin(π+x) = sin(x) - (-sin(x)) + 2(-sin(x)) = sin(x) + sin(x) - 2sin(x) = 2sin(x) - 2sin(x) = 0
So, Cos(π/2-x) - sin(-x) + 2sin(π+x) equals 0.