Question

How do you prove `Cos^2 2A-cos^2 A=sin^2A-sin^2 2A`?

Answer 1

It is proved by `sin^2theta+cos^2theta=1`

Explanation:

LHS=`cos^2(2A)-cos^2(A)`

LHS=`1-sin^2(2A)-(1-sin^2A)`

LHS=`1-sin^2(2A)-1+sin^2A`

LHS=`sin^2A-sin^2(2A)`

LHS=RHS