Evaluate exactly and simplify the following Write your answe

Evaluate exactly and simplify the following. Write your answer as a reduced improper fraction if needed. Use squareroot () for Squareroot () if needed. sin(2tan^-1(13/10)).

Solution

sin(2tan^-1(13/10))

Let tan^-1(13/10)=x   therefore tan x=13/10

here opposite=13    and adjacent=10

Hence hypotenuse=sqrt(13²+10²) = sqrt269

sinx=opposite/hypotenuse= 13/sqrt269

cos x= adjacent/hypotenuse=10/sqrt269

sin(2x)=2sinx cos x=2(13/sqrt269)(10/sqrt269)=260/269