Question

tan(2tan^-1(1/5+π/4))​

Answer 1

Using the identity:

2 tan^-1(x)=tan^-1(2x/1-x^2)

tan(2tan^-1(1/5+π/4))

Here, x=1/5+π/4

tan(tan^-1(2×{1/5+π/4}))

=tan(tan^-1(2×{4+5π}/20)

=tan(tan^-1{4+5π}/10)

Also, tan(tan^-1(x))=x

So the expression becomes:

(4+5π)/10

or 2/5+π/2