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Question

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

A
257
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B
2512
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C
2513
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D
247
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Solution

The correct option is D 247
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

α+β2=247

Hence, option 'D' is correct.

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