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Question

If tanα=xx+1 and tanβ=12x+1, then α+β is equal to


A

π2

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B

π3

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C

π6

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D

π4

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Solution

The correct option is D

π4


Given that:
tanα=xx+1 and tanβ=12x+1
Now, tan(α+β)=tanα+tanβ1tanα+tanβtan(α+β)=xx+1+12x+11(xx+1)(x2x+1)tan(αβ)=x(2x+1)+x+1(x+1)(2x+1)2xtan(α+β)=2x2+x+x+12x2+2x+x+1xtan(α+β)=2x2+x+x+12x2+2x+1tan(α+β)=1 α+β=π4


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