Question 837012: Simplify tan(sin^(-1) x) also written as tan(arcsinx)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! To avoid confusion I will switch the sin to "t":::
Simplify tan(sin^(-1) t) also written as tan(arcsinx)
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sin[sin^-1(t)) = t/1
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By defination, sin = y/r, so y = t and r = 1
Then x = sqrt[1^2-t^2]
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Finally: By definition, tan(t) = y/x
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So tan(t) = t/sqrt(1-t^2)
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Cheers,
Stan H.
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