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Question

If sin(α+β)=1,sin(αβ)=1/2, then tan(α+2β)tan(2α+β)=

A
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Solution

The correct option is A 1
sin(α+β)=1,sin(αβ)=1/2
α+β=π/2,αβ=π/6
α=π3,β=π6
=tan(α+2β)tan(2α+β)
=tan(2π3)tan(5π6)
=(3)(1/3)=1

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