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

1 Answer
Feb 9, 2016

Explanation given below.

Explanation:

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.