Math, asked by aniruddhdubeydd123, 7 months ago

Cos 2 alpha into cos 2 beta + sin square alpha minus beta minus sin square alpha + beta is equal to cos lambda alpha + beta; find lambda

Answers

Answered by itzcrazyboy47
2

Answer:

Answer:To Prove: [tex]cos\,2\alpha\;cos\,2\beta+sin^2\,(\alpha-\beta)-sin^2\,(\alpha+\beta)=cos\,2(\

Answered by Amrit111Raj82
4

Identity

sin

2

A−sin

2

B

=sin(A+B)sin(A−B)

=(sin(A)+sin(B))(sin(A)−sin(B))

=2sin(

2

A+B

)cos(

2

A−B

).2cos(

2

A+B

)sin(

2

A+B

)

=2sin(

2

A+B

)cos(

2

A+B

).2sin(

2

A−B

)cos(

2

A−B

)

=sin(A+B)sin(A−B)

Given equation

sin

2

α+[sin

2

β−sin

2

γ]

=sin

2

α+sin(β−γ)sin(β+γ)

=sin

2

α+sin(π−α)sin(β+γ)

=sin

2

α+sinαsin(β+γ)

=sinα[sinα+sin(β+γ)]

=sinα[sin(π−(β−γ))+sin(β+γ)]

=sinα[sin(β−γ)+sin(β+γ)]

=sinα[2sinβcosγ]

=2sinαsinβcosγ

∴λ=2

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