( c o s α + c o s β ) 2 + ( s i n α + s i n β ) 2 = Options: A . &nbsp 4 c o s 2 α − β 2 B . &nbsp 4 s i n 2 α − β 2 C . &nbsp 4 c o s 2 α + β 2 D . &nbsp 4 s i n 2 α + β 2

(cosα+cosβ)2+(sinα+sinβ)2 =

Question

$(c o s α + c o s β)^{2} + (s i n α + s i n β)^{2}$ =

Options:

A .

4 c o s^{2}

\frac{α - β}{2}

B .

4 s i n^{2}

\frac{α - β}{2}

C .

4 c o s^{2}

\frac{α + β}{2}

D .

4 s i n^{2}

\frac{α + β}{2}

Answer: Option A
:
A

$(c o s α + c o s β)^{2} + (s i n α + s i n β)^{2}$

= $c o s^{2} α + c o s^{2} β + 2 c o s α c o s β + s i n^{2} α + s i n^{2} β + 2 s i n α s i n β$

= $2 (1 + c o s (α - β))$ = $4 c o s^{2} (\frac{α - β}{2})$ .

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