InterviewSolution
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InterviewSolution
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`sin^(-1)[(sqrt(1+x)+sqrt(1-x))/(2)]` का x के सापेक्ष अवकल गुणांक ज्ञात कीजिए। |
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Answer» माना `y=sin^(-1)[(sqrt(1+x)+sqrt(1-x))/(2)]` और `x=cos theta` `therefore " "y=sin^(-1)[(sqrt(1+costheta)+sqrt(1-costheta))/(2)]` `" "=sin^(-1)[(sqrt(2cos^(2).(theta)/(2))+sqrt(2sin^(2).(theta)/(2)))/(2)]` `" "=sin^(-1)[(1)/(sqrt2)cos.(theta)/(2)+(1)/(sqrt2)sin.(theta)/(2)]` `" "=sin^(-1)[sin.(pi)/(4)cos.(theta)/(2)+cos.(pi)/(4)sin.(theta)/(2)]` `" "=sin^(-1)sin((pi)/(4)+(theta)/(2))=(pi)/(4)+(theta)/(2)=(pi)/(4)+(1)/(2)cos^(-1)x` `rArr" "(dy)/(dx)=(d)/(dx)((pi)/(4)+(1)/(2)cos^(-1)x)` `=0+(1)/(2)((-1)/(sqrt(1-x^(2))))=(-1)/(2sqrt(1-x^(2)))` |
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