How do you find the exact value of sin(tan^-1(sqrt3/3))sin(tan−1(√33))?

1 Answer
Binayaka C.
Oct 11, 2016

The exact value of sin(tan^-1(sqrt3/3)) =1/2sin(tan−1(√33))=12

Explanation:

sin(tan^-1(sqrt3/3))sin(tan−1(√33)). Let tan^-1(sqrt3/3)=theta :. tan theta=sqrt3/3
We know tantheta= perpendicular/base=sqrt3/3 :.Hypotenuse = sqrt(3^2+(sqrt3^2))= sqrt12=2sqrt2 :. sin theta=perp./hypotenuse =sqrt3/(2sqrt3)=1/2 :.theta=sin^-1(1/2)
Hence sin(tan^-1(sqrt3/3)) = sin(sin^-1(1/2))=1/2 [Ans]

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