Question

tan inverse [(x-1)÷(x-2)]+tan inverse[(x+1)÷(x+2)] find x​

Answer 1

Answer:

Let A=tan

−1

x−2

x−1

and B=tan

−1

x+2

x+1

Now,

tan(A+B)=tan

4

π

∴

1−tanAtanB

tanA+tanB

=1

∴tanA+tanB=1−tanAtanB

∴

x−2

x−1

+

x+2

x+1

=1−

x−2

x−1

×

x+2

x+1

∴(x−1)(x+2)+(x+1)(x−2)=1−(x−1)(x+1)

∴x

2

+x−2+x

2

−x−2=x

2

−4−x

2

+1

∴2x

2

=1

∴x=±

2

1