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Question

If tan1(x1x2)+tan1(x+1x+2)=π4, find the value of x

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Solution

We have,

tan1(x1x2)+tan1(x+1x+2)=π4

We know that

tan1x+tan1y=tan1x+y1xy

Therefore,

tan1(x1x2)+(x+1x+2)1(x1x2)(x+1x+2)=π4

(x1)(x+2)+(x+1)(x2)(x+2)(x2)(x2)(x+2)(x1)(x+1)(x+2)(x2)=tanπ4

x2+2xx2+x22x+x2x24x2+1=1

2x243=1

2x24=3

2x2=1

x2=12

x=±12

Hence, this is the value.


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