Question

Find the value of `sin(2tan^-1  2/3) + cos(tan^-1 sqrt(3))`

Answer 1

Let `tan-1  2/3` = x and `tan^-1 sqrt(3)` = y

So that tan x = `2/3` and tan y = `sqrt(3)`

Therefore, `sin(2tan^-1  2/3) + cos(tan^-1 sqrt(3))`

= sin (2x) + cos y

= `(2tanx)/(1 + tan^2x)+/sqrt(1 +tan^2y)`

= `(2*2/3)/(1 + 4/9) + 1/( + sqrt((sqrt(3))^2`

= `12/13 +1/2`

= `37/26`.