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Prove that Cos^4 A- sin^4 A=cos 2A |
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Answer» We use the FOLLOWING identities a 2 n − b 2 n = ( a n + b n ) ( a n − b n )
sin 2 x + cos 2 x = 1
cos ( a + b ) = cos a cos b − sin a sin b
Proof cos 4 x − sin 4 x = ( cos 2 x + sin 2 x ) ( cos 2 − sin 2 x ) = cos 2 x − sin 2 x = cos x cos x − sin x sin x = cos ( x + x ) = cos 2 x |
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