InterviewSolution
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InterviewSolution
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`cos^(-1)(2xsqrt(1-x^(2)))` |
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Answer» Let `y=cos ^(-1)(2xsqrt(1-x^(2)))` Put ` x=sin theta` `thereforetheta=sin^(-1)x ` `y=cos^(-1)(2sinthetasqrt(1-sin^(2)theta))` `y=cos^(-1)(2sin thetacostheta)` `y=cos^(-1)(sin 2theta)` `y=cos ^(-1)[cos ((pi)/(2)-2theta)]` `y=pi/2-2theta` `y=pi/2-2sin ^(-1)x` `therefore (dy)/(dx)=(-2)/(sqrt(1-x^(2)))` |
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