Trigonometry question

Someone please help me with this question:

Show that cos θ (1-cosθ) = sin θ sinθ
2 2

Thanks in advance :smile:

I assume that the right hand side is (sinθ)^2, what you would first do is expand the left hand side so you get cosθ - (cosθ)^2 = (sinθ)^2.

Using the trig identity that (sinθ)^2 + (cosθ)^2 = 1, we get that (sinθ)^2 = 1- (cosθ)^2

Sub this into our equation and we get cosθ - (cosθ)^2 = 1- (cosθ)^2, this is quite nice because the squared terms cancel leaving us with cosθ = 1

Arccos(1) = 0, 360 or 2π =θ

Reply 2

davros

Original post by Sara_546

Someone please help me with this question:

Show that cos θ (1-cosθ) = sin θ sinθ
2 2

Thanks in advance :smile:

Could you upload a picture of the actual question because what you've typed really isn't clear!

Are you trying to prove an identity or solve an equation?