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Question

Let tanα=aa+1 and tanβ=12a+1, then α+β is

A
π4
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B
π3
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C
π2
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D
π
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Solution

The correct option is D π4
Given, tanα=aa+1 and tanβ=12a+1
tan(α+β)=tanα+tanβ1tanαtanβ
=aa+1+12a+11aa+1×12a+1
=a(2a+1)+(a+1)(a+1)(2a+1)a
=2a2+2a+12a2+2a+1=1α+β

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