Question

prove that cos(α+β)+cos^2β-2cos(α-β)cosα.cosβis independent ofβ​

Answer 1

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MATHS

Prove that cos2α=2sin

2

β+4cos(α+β)sinαsinβ+cos2(α+β)

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ANSWER

2sin

2

β+4cos(α+β)sinαsinβ+cos2(α+β)

=2sin

2

β+2cos(α+β)(cos(α−β)−cos(α+β))+cos2(α+β)

=2sin

2

β+2cos(α+β)cos(α−β)−2cos

2

(α+β)+cos2(α+β)

=2sin

2

β+2cos

2

α−2sin

2

β−2cos

2

(α+β)−2cos

2

(α+β)−1

=2cos

2

α−1=cos2α