How would you simplify tan(sin^-1 (x/2)) to find its exact value?
Is sin^2 theta+cos theta=2 true or false?

Question

How would you simplify tan(sin^-1 (x/2)) to find its exact value?
Is sin^2 theta+cos theta=2 true or false?

anonymous · Answer

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anonymous · Answer

there is a picture of an angle whose sine is $\frac{x}{2}$ 
find the third side via pythagoras
then you can find any trig ratio you want

anonymous · Answer

Does it matter that it's sin^-1?

anonymous · Answer

not sure what you are asking 
but i guess the answer is "of course it matters" if it was cosine it would be different

anonymous · Answer

did you find the third side?

anonymous · Answer

i think maybe i lost you there
?

anonymous · Answer

Sorry, I spent some time doing the calculation with identities instead of a triangle and ended up with 
$$ \tan(\sin^-1 x/2)= (x/2)/(√1-(x^2/4))=x/(2√(1-(x^2/4)))$$
Would this result in the same answer as using the triangle?

amilapsn · Answer

yep