( + )^2 + ( + )^2 = - Vidyadip

MCQ

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

✓
$4{\cos ^2}\frac{{\alpha - \beta }}{2}$
B
$4{\sin ^2}\frac{{\alpha - \beta }}{2}$
C
$4{\cos ^2}\frac{{\alpha + \beta }}{2}$
D
$4{\sin ^2}\frac{{\alpha + \beta }}{2}$

✓

Answer

Correct option: A.

$4{\cos ^2}\frac{{\alpha - \beta }}{2}$

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

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

${\sin ^2}\beta + 2\sin \alpha \sin \beta $

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

$= 4{\cos ^2}\left( {\frac{{\alpha - \beta }}{2}} \right)$.

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