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Question
Write the following in the simplest form:
`sin{2tan^-1sqrt((1-x)/(1+x))}`
Solution
Let x = cos θ
Now,
`sin{2tan^-1sqrt((1-x)/(1+x))}=sin{2tan^-1sqrt((1-costheta)/(1+costheta))}`
`=sin{2tan^-1sqrt((2sin^2 theta/2)/(2cos^2 theta/2))}`
`=sin{2tan^-1(tan theta/2)}`
= sin θ
= sin (cos-1 x)
`=sin(sin^-1(sqrt(1-x^2)))`
`=sqrt(1-x^2)`
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