Question

Find the value of tan [ 1/3( tan^-1x + tan^-1(1/x))]​

Answer 1

Answer:

1/√3

Step-by-step explanation:

let tan⁻¹x=A then tanA = x

1/x=cotA=tan(90-A)

=tan⁻¹ 1/x) - tan⁻¹ { tan(90-A) }=90-A

Hence tan [ 1/3( tan⁻¹x + tan⁻¹(1/x))]​

=tan( 1/3 ( A+90-A)

=tan(90/3)=tan30

=1/√3