If cos-cos-2-sin-sin-2-cos 2-2- write tha value of -

We have, LHS=(cosα +cosβ )^2+(sinα +sinβ )^2 = [ 2cos ( α +β/2 )cos ( α β/2 ) ]^2 [ 2sin ( α +β/2 )cos ( α β/2 ) ]^2 =4cos^2 ( α +β/2 )cos^2 ( α β/2 )+4s ...

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Byju's Answer

Standard XII

Mathematics

Cos(A+B)Cos(A-B)

If cosα+cosβ2...

Question

If $(c o s α + c o s β)^{2} + (s i n α + s i n β)^{2} = λ c o s^{2} (\frac{α - β}{2})$ , write tha value of $λ$

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Solution

We have,
$L H S = (c o s α + c o s β)^{2} + (s i n α + s i n β)^{2} = {[2 c o s (\frac{α + β}{2}) c o s (\frac{α - β}{2})]}^{2} {[2 s i n (\frac{α + β}{2}) c o s (\frac{α - β}{2})]}^{2} = 4 c o s^{2} (\frac{α + β}{2}) c o s^{2} (\frac{α - β}{2}) + 4 s i n^{2} (\frac{α + β}{2}) c o s^{2} (\frac{α - β}{2}) = 4 c o s^{2} (\frac{α - β}{2}) [c o s^{2} (\frac{α + β}{2}) + s i n^{2} (\frac{α + β}{} 2)] = 4 c o s^{2} (\frac{α - β}{2}) [∵ c o s^{2} + θ + s i n^{2} θ = 1] \Rightarrow (c o s α + c o s β)^{2} + (s i n α + s i n β)^{2} = 4 c o s^{2} (\frac{α - β}{2})$
It is given that,
$(c o s α + c o s β)^{2} + (s i n α + c o s β)^{2} = λ c o s^{2} (\frac{α - β}{2})$
On comparing, we get
$λ = 4 ∴ λ = 4$

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Similar questions

{(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})

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

Find b

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

k {cos}^{2} (\frac{α - β}{2})

, then k is equal to

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

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If (cosα+cosβ)2+(sinα+sinβ)2=λcos2(α−β2), write tha value of λ

If $(c o s α + c o s β)^{2} + (s i n α + s i n β)^{2} = λ c o s^{2} (\frac{α - β}{2})$ , write tha value of $λ$