The correct option is A 4 cos^2 α β/2 (cos α + cos β)^2 + (sin α + sin β)^2 = cos^2 α + cos^2 β + 2 cos α cos β + sin^2 α + sin^2 β + 2 sin α sin β = 2(1 + ...

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Byju's Answer

Standard XI

Mathematics

Conditional Identities

cosα+cosβ2+si...

Question

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

$4 c o s^{2}$ $\frac{α - β}{2}$

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$4 s i n^{2}$ $\frac{α - β}{2}$

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$4 c o s^{2}$ $\frac{α - β}{2}$

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$4 s i n^{2}$ $\frac{α + β}{2}$

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Solution

The correct option is A
$4 c o s^{2}$ $\frac{α - β}{2}$

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

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

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

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Similar questions

{(cos α + cos β)}^{2} + {(sin α + sin β)}^{2} = . . . . . . . . .

(cos α - cos β)^{2} + (sin α - sin β)^{2}

reduces to:

Q. Simplify

(cos α - cos β)^{2} + (sin α - sin β)^{2}

reduces to :

{(cos α - cos β)}^{2} + {(sin α - sin β)}^{2} = 4 {sin}^{2} {(α - β) / 2}

Q. Prove that,

{(cos α + cos β)}^{2} + {(sin α + sin β)}^{2} = 4 {cos}^{2} (\frac{α - β}{2})

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(cosα+cosβ)2+(sinα+sinβ)2 =

The correct option is A 4cos2 α−β2 (cosα+cosβ)2+(sinα+sinβ)2 = cos2α+cos2β+2cosαcosβ+sin2α+sin2β+2sinαsinβ = 2(1+cos(α−β)) = 4cos2(α−β2).

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

The correct option is A
$4 c o s^{2}$ $\frac{α - β}{2}$

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

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

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