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Question

Solve for x the following :
(a) tan1x1x2+tan1x+1x+2=π4
(b) tan1x1x+1+tan12x12x+1=tan12336

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Solution

(a)

=tan1(x1x2)+tan1(x+1x+2)

=tan1⎜ ⎜ ⎜x1x2+x+1x+21x1x2×x+1x+2⎟ ⎟ ⎟

=tan1(2x243)

=π4

(2x243)=tan1π4

(2x243)=1

2x24=3

x2=12

x=12

(b)

=tan1(x1x+1)+tan1(2x12x+1)

=tan1⎜ ⎜ ⎜x1x+1+2x12x+11x1x+1×2x12x+1⎟ ⎟ ⎟

=tan1(4x226x)

=tan12336

(4x226x)=2336

6(4x22)=23x

24x223x12=0

Solving the quadratic equation, we get,

x=43 and x=38

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