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Question

Considering principal values, the number of solutions of tan12x+tan13x=π4 is

A
two
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B
three
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C
one
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D
none of these
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Solution

The correct option is C one
Given, tan1(2x)+tan1(3x)=π4
tan1(5x16x2)=π4
Taking tan on both the sides, we get
5x16x2=1
5x=16x2
6x2+5x1=0
6x2+6xx1=0
(6x1)(x+1)=0
x=1 and x=16.

By considering the principal values, only x=1/6 is possible
Hence there will be one real value of x.

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