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Question

Solve : tan1(x1x2)+tan1(x+1x+2)=π4

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Solution

tan1(x1x2)+tan1(x+1x+2)=π4

tan1a+tan1b=tan1(a+b1ab)

tan1⎜ ⎜ ⎜ ⎜ ⎜(x1)(x2)+(x+1)(x+2)1(x1x2)(x+1x+2)⎟ ⎟ ⎟ ⎟ ⎟=π4

(x1)(x+2)+(x+1)(x2)(x24)(x21)=tanπ4

x2+x2+x2x2(4+1)=1

2x24=3

2x2=1

x=±12

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