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Question

If αβ=3π4 then (1tanα)(1+tanβ)=

A
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B
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C
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2
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Solution

The correct option is B 2
αβ=3π4
tan(αβ)=tan3π4
tanαtanβ1+tanαtanβ=1
tanαtanβ=1tanαtanβ
tanβtanα1tanαtanβ=0
1+tanβ+1tanαtanαtanβ=1
(1+tanβ)tanα(1+tanβ)=2
(1tanα)(1+tanβ)=2.

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