InterviewSolution
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InterviewSolution
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`tan^(-1)((2x)/(1-x^(2)))` का `cos^(-1)((1-x^(2))/(1+x^(2)))` के सापेक्ष अवकल गुणांक ज्ञात कजिए । |
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Answer» माना `y_(1)=tan^(-1).(2x)/(1-x^(2))` `=2tan^(-1)x` `rArr" "(dy_(1))/(dx)=2.(d)/(dx)tan^(-1)x=(2)/(1+x^(2))` माना `y_(2)=cos^(-1)((1-x^(2))/(1+x^(2)))` माना `x=tan theta` `therefore" "y_(2)=cos^(-1)((1-tan^(2)theta)/(1+tan^(2)theta))` `=cos^(-1)(cos2 theta)=2 theta=2tan^(-1)x` `rArr" "(dy_(2))/(dx)=2(d)/(dx).tan^(-1)x=(2)/(1+x^(2))` अब `" "(dy_(1))/(dy_(2))=(dy_(1)//dx)/(dy_(2)//dx)=(2//(1+x^(2)))/(2//(1+x^(2)))=1` |
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