Expert: Paul Klarreich - 11/17/2009

Question
Hi, can you please help me in this question?
It says prove:
cos^2theta = 1/2 + 1/2cos2theta
Thanks

Answer
Questioner: Rabia
Country: Canada
Category: Calculus
Private: No
Subject: Double Angle Formulas
Question: Hi, can you please help me in this question?
It says prove:
cos^2theta = 1/2 + 1/2cos2theta
Thanks
.....................................
Hi, Rabia,

cos^2(t) = 1/2 + 1/2cos(2t)   << proper notation.

I assume you have memorized this double-angle formula: (yes, you have to memorize things like that)

cos(2t) = 2 cos^2(t) - 1

Substitute:

cos^2(t) = 1/2 + 1/2[2 cos^2(t) - 1]

Remove parentheses:

cos^2(t) = 1/2 + cos^2(t) - 1/2

Simplify:

cos^2(t) = cos^2(t)

Finito.