How do you evaluate sin(tan^-1(12/5))sin(tan−1(125))?

1 Answer
Binayaka C.
Jan 31, 2017

sin (tan^-1(12/5)) =12/13sin(tan−1(125))=1213

Explanation:

sin (tan^-1(12/5))sin(tan−1(125)). Let tan^-1(12/5) = theta :. tan theta = 12/5
Since tan^-1 exists in 1st quadrant & 4th quadrant and positive in 1st quadrant, theta is in 1st quadrant . we know tan theta =p/b= 12/5 :. p=12 ; b=5 ; h= sqrt(p^2+b^2)=sqrt(12^2+5^2)=13 ; sin theta = p/h=12/13. [p=perpendicular ; b = base; h= hypotenuse]

:.sin (tan^-1(12/5)) =sin theta = 12/13 [Ans]

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