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