How do you verify #Cos 2x= 2 sin (x+pi/4) cos (x+pi/4)#?

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Answer 1 · 2016-02-09T06:33:24

Explanation given below.

Verify #cos(2x) = 2sin(x+pi/4)cos(x+pi/4)#

First let us understand two identities

#color(Blue)(sin(2theta)=2sin(theta)cos(theta)#

#color(Blue)(sin(pi/2 + theta) =cos(theta)#

Now let us take our problem

#cos(2x) = 2sin(x+pi/4)cos(x+pi/4)#

Let us start with the Right Hand side

#= 2sin(x+pi/4)cos(x+pi/4)#

#=sin(2(x+pi/4)# double angle formula for sine.

#=sin(2x+pi/2)#

#=cos(2x)quad# by the second identity shared above.