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"#