Question

solve this please: ?​

Answer 1

Step-by-step explanation:

Given,

$( \cos( \alpha ) + \cos( \beta )) ^{2} + ( \sin( \alpha ) + \sin( \beta ) )^{2}$

$= > \cos^{2} ( \alpha ) + \cos ^{2} ( \beta ) + 2 \cos( \alpha ) \cos( \beta ) + \sin^{2} ( \alpha ) + \sin^{2} ( \beta ) + 2 \sin( \alpha ) \sin( \beta )$

We know that, Sin²θ+Cos²θ=1, so,

$= > 1 + 1 + 2 \sin( \alpha ) \sin( \beta ) + 2 \cos( \alpha ) \cos( \beta )$

By using, cos(x-y)=cos(x)cos(y)+sin(x)sin(y), we get,

$= > 2 + 2( \cos( \alpha - \beta ) )$

$= > 2(1 + \cos( \alpha - \beta ))$

We also know that, cos(2x)=2cos²(x)-1 =>1+cos(2x)=2cos²(x)

So,

$= > 2.2 \cos^{2} ( \frac{ \alpha - \beta }{2} )$

$= > 4 \cos^{2} ( \frac{ \alpha - \beta }{2} )$

Hence, proved