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Question

If θ+α=π/4, then (tanθ+1)(tanα+1) is equal to

A
1
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B
2
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C
3
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D
None of these
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Solution

The correct option is A 2
If θ+α=π4 θ=π4α
(tanθ+1)(tanα+1)
=(tan(π4α)+1)(tanα+1)
=tanα.tan(π4α)+tan(π4α)+tanα+1
=tanα(1tanα1+tanα)+1tanα1+tanα+(tanα+1)
=tanαtan2α+1tanα+tan2α+2+tanα+1(1+tanα)
=2(tanα+1)(tanα1)
=2

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