Show the identity cos(2a)=1-2sin^2a can be derived form a sum or difference identity and the pythagorean identity?

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doesnt make sense

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Answer 1 · 2018-05-01T00:13:43

Yes, can do, see below

#cos(2a)=1-2sin^2a#

Use cosine sum identity :
#cos(a+a)=1-2sin^2a#

#cosacosa-sinasina=1-2sin^2a#

#cos^2a-sin^2a= 1-2sin^2a#

Apply modified pythagorean identity : #cos^2x=1-sin^2x#

#(1-sin^2a)-sin^2a= 1-2sin^2a#

#1-2sin^2a= 1-2sin^2a#