How do you verify $cos ^2 u - sin ^2 u = 2 cos^2 u -1$ ?

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Answer 1 · 2015-06-09T07:59:58

We know that $sin^2u + cos^2 u =1$

LHS= - ( $sin^2u - cos^2 u$ )
= - { $(1-cos^2u) - cos^2 u$ } [ since $sin^2u + cos^2 u =1$ ]
= $2cos^2u-1$
=RHS

Hence proved

How do you verify cos ^2 u - sin ^2 u = 2 cos^2 u -1cos ^2 u - sin ^2 u = 2 cos^2 u -1?