How do you evaluate $sin(sin^-1(-1/sqrt2))$ ?

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Answer 1 · 2017-06-20T10:40:07

$sin(sin^-1 (-1/sqrt2)) = -1/sqrt2$

$sin(sin^-1 (-1/sqrt2))$ .

Let $sin^-1 (-1/sqrt2) = theta :. sin theta = (-1/sqrt(2))$

We know $sin(pi/4)=1/sqrt2 , sin(-pi/4)= -1/sqrt2$

$:. sin theta = sin (-pi/4) :. theta = -pi/4 :. sin^-1 (-1/sqrt2) = -pi/4$

$sin(sin^-1 (-1/sqrt2)) = sin (-pi/4) = -1/sqrt2$ [Ans]

How do you evaluate sin(sin^-1(-1/sqrt2))sin(sin^-1(-1/sqrt2))?