Question

-2sin x/2 cos x/2 =1-sin x . how do I verify this?

Answer 1

[cos(x/2) - sin(x/2)]^2 = 1 - sinx
cos^2(x/2) - 2cos(x/2)sin(x/2) + sin^2(x/2)
cos^2(x/2) + sin^2(x/2) - 2cos(x/2)sin(x/2)
1 - 2cos(x/2)sin(x/2)
1- sin(2x/2)
1- sin(x) <= equal to the right side...

Answer 2

using the double angle formula: 2sin(u) cos(u) = sin(2u)
apply it here............................2 sin(x/2) cos(x/2) = sin[2(x/2)] = sin(x)

Answer 3

thank you so much!

Answer 4

You're welcome!

Answer 5

:)