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Question

Solve :tan14x+tan16x=π4

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Solution

tan14x+tan16x=π4
tan1(4x+6x124x2)=π4, provided 4x×6x<14x+6x124x2=tan1(π4)10x124x2=1(12x1)(2x+1)=0x=112,12

For x=112, 4x×6x=16<1
For x=12, 4x×6x=61
Therefore, the solution of the given equation is x=112



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