Sin^2x=1/2(1-Cos2x) - Math Central

HOME

Math Central

Quandaries & Queries

Question from Chris:

I have tried and tried and tried to do this question and am losing my will to live with trigonometric identities could someone please show a step by step guide on how to answer this question
Thanks chris
Sin^2x=1/2(1-Cos2x) and then explain where this identity would be useful???

Hi Chris,

When I see this question I realize that I need to express cos(2x) in terms of sin(x) and cos(x). I know that

cos(2x) = cos²(x) - sin²(x)

But the left side has only sin²(x) and no cosines so in the expression for cos(2x) above I can use the act that

sin²(x) + cos²(x) = 1 or cos²(x) = 1 - sin²(x)

to eliminate the cosine term. So here is how my solution starts

1/2(1-Cos2x) = 1/2(1- [cos²(x) - sin²(x)]) = 1/2(1- cos²(x) + sin²(x))

Can you complete it?

Harley

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.