Sunday, 6 August 2017

trigonometry - Proving A Trigonometric Identity- Double Angles



(cos(2x)sin(2x))(sin(2x)+cos(2x))=cos(4x) I'm trying to prove that the left side equals the right side. I'm just stuck on which double angle formula of cosine to use.


Answer



(cos(2x)sin(2x))(sin(2x)+cos(2x))=(cos2(2x)sin2(2x))=cos(4x)
From
cos(a+b)=cosacosbsinasinb if a=2x,b=2x then

cos(4x)=cos22xsin22x


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