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Question

If 3sinα=5sinβ, then tanα+β2tanαβ2 is equal to

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is D 4
3sinα=5sinβ
sinαsinβ=53
Using componendo and dividendo
sinα+sinβsinαsinβ=5+353=4


2sin(α+β2)cos(αβ2)2sin(αβ2)cos(α+β2)=4


tan(α+β2)tan(αβ2)=4



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