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Question

If tan1a+xa+tan1axa=π6, then x2=?

A
23a
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B
3a
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C
23a2
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D
None of these
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Solution

The correct option is C 23a2
tan1(a+xa)+tan1(axa)=π6

tan1(a+xa+axa)(1(a+xa)(axa))=π6

tan1⎜ ⎜ ⎜2aa11a2x2a2⎟ ⎟ ⎟=π6

tan1(2a2a2a2+x2)=π6

2a2x2=tanπ6

x2=2a213

x2=23a2

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