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Question

If sinα+sinβ=14 and cosα+cosβ=13, then the value of sin(α+β) is,

A
2425
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B
1325
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C
1213
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D
none of these
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Solution

The correct option is A 2425
sinα+sinβ=14.....(1)

2sin(α+β2)cos(αβ2)=14

cosα+cosβ=13..........(2)

2cos(α+β2)cos(αβ2)=13

Dividing (1) by (2), we get

2sin(α+β2)cos(αβ2)2cos(α+β2)cos(αβ2)=34

tan(α+β2)=34

Using sin2x=2tanx1+tan2x

sin(α+β)=2341+(34)2=2425

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