How do you verify the identity $cos^2beta-sin^2beta=2cos^2beta-1$ ?

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Answer 1 · 2017-01-28T09:22:31

to prove $cos^2beta-sin^2beta=2cos^2beta-1---(1)$

now $cos^2beta+sin^2beta=1$

we have $" "sin^2beta=1-cos^2beta$

substitute for $sin^2beta" "$ on the $LHS" in "---(1)$

we have

$cos^2beta-(1-cos^2beta)$

$=cos^2beta-1+cos^2beta$

giving

$2cos^2beta-1" as required"$

How do you verify the identity cos^2beta-sin^2beta=2cos^2beta-1cos^2beta-sin^2beta=2cos^2beta-1?