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it can be written as sin^-1(2x/1+x^2)
put x=tan theta
sin^-1(2tantheta/1+tan^2theta)
sin^-1(2tantheta/sec^2theta)
sin^-1(2sintheta/costheta ×cos^2theta)
sin^-1(2sinthetacostheta)
sin^-1(sin2theta)
= 2theta
2tan^-1(x) is answer
put x=tan theta
sin^-1(2tantheta/1+tan^2theta)
sin^-1(2tantheta/sec^2theta)
sin^-1(2sintheta/costheta ×cos^2theta)
sin^-1(2sinthetacostheta)
sin^-1(sin2theta)
= 2theta
2tan^-1(x) is answer
kapoor181282p63ys0:
correct and is tan^-1(x)
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