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Question

If α+β=45θ then (1+tanα)(1+tanβ)=

A
1 /2
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B
3
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C
0
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D
2
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Solution

The correct option is D 2
tan(α+β)=tanα+tanβ1tanαtanβ

tan(45)=1=tanα+tanβ1tanαtanβ

1tanαtanβ=tanα+tanβ

1=tanα+tanβ+tanαtanβ

=(1+tanα)(1+tanβ)1

(1+tanα)(1+tanβ)=1+1=2.

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