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

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Answer 1 · 2015-07-05T15:26:20

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

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

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