How do you verify $cos 2 x = 2 sin (x + \frac{π}{4}) cos (x + \frac{π}{4})$ $Cos 2x= 2 sin (x+pi/4) cos (x+pi/4)$ ?

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How do you verify $cos 2 x = 2 sin (x + \frac{π}{4}) cos (x + \frac{π}{4})$ $Cos 2x= 2 sin (x+pi/4) cos (x+pi/4)$ ?

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Answer 1 · 2016-02-09T06:33:24

Explanation given below.

Explanation:

Verify $cos (2 x) = 2 sin (x + \frac{π}{4}) cos (x + \frac{π}{4})$ $cos(2x) = 2sin(x+pi/4)cos(x+pi/4)$

First let us understand two identities

$sin (2 θ) = 2 sin (θ) cos (θ)$ $color(Blue)(sin(2theta)=2sin(theta)cos(theta)$

$sin (\frac{π}{2} + θ) = cos (θ)$ $color(Blue)(sin(pi/2 + theta) =cos(theta)$

Now let us take our problem

$cos (2 x) = 2 sin (x + \frac{π}{4}) cos (x + \frac{π}{4})$ $cos(2x) = 2sin(x+pi/4)cos(x+pi/4)$

Let us start with the Right Hand side

$= 2 sin (x + \frac{π}{4}) cos (x + \frac{π}{4})$ $= 2sin(x+pi/4)cos(x+pi/4)$

$= sin (2 (x + \frac{π}{4})$ $=sin(2(x+pi/4)$ double angle formula for sine.

$= sin (2 x + \frac{π}{2})$ $=sin(2x+pi/2)$

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

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How do you verify $cos 2 x = 2 sin (x + \frac{π}{4}) cos (x + \frac{π}{4})$ $Cos 2x= 2 sin (x+pi/4) cos (x+pi/4)$ ?

1 Answer

Explanation:

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How do you verify Cos 2x= 2 sin (x+pi/4) cos (x+pi/4)cos2x=2sin(x+π4)cos(x+π4)Cos 2x= 2 sin (x+pi/4) cos (x+pi/4)?

1 Answer

Explanation:

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How do you verify $cos 2 x = 2 sin (x + \frac{π}{4}) cos (x + \frac{π}{4})$ $Cos 2x= 2 sin (x+pi/4) cos (x+pi/4)$ ?