Question

If sinα+ sinβ=a and cosα- cosβ=b then tan(a-b)/2=

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Answer 1

Answer:

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Asked on December 26, 2019 by

Jyothi Rithvick

If sinα+sinβ=a and cosα+cosβ=b, then the value of sinα+β=

a

2

+b

2

mab

.Find m

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ANSWER

sinα+sinβ=a,cosα+cosβ=b

a

2

+b

2

=sin

2

α+sin

2

β+cos

2

α+cos

2

β+2(sinαsinβ+cosαcosβ)

a

2

+b

2

=2+2cos(α−β)

∴1+cos(α−β)=

2

a

2

+b

2

ab=sinαcosα+sinαcosβ+sinβcosα+sinβcosβ

=sin(α+β)+

2

sin2α+sin2β

=sin(α+β)+sin(α+β)cos(α−β)

=sin(α+β)[1+cos(α−β)]

ab=sin(α+β)(

2

a

2

+b

2

)

∴sin(α+β)=

a

2

+b

2

2ab

Given,

sin(α+β)=

a

2

+b

2

mab

∴m=2

Step-by-step explanation:

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Answer 2

Answer:

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