InterviewSolution
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InterviewSolution
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यदि `y=sin^(-1)((1)/(sqrt(1+x^(2))))+tan^(-1)((sqrt(1+x^(2))-1)/(x))`, `(dy)/(dx)` निकालें। |
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Answer» Correct Answer - `-(1)/(2(1+x^(2)))` `x=tantheta` रखने पर हमें मिलता है, `y=sin^(-1){(1)/(sqrt(1+tan^(2)theta))}+tan^(-1){(sqrt(1+tan^(2)theta)-1)/(tantheta)}` `=sin^(-1)(costheta)+"tan"^(-1)(1-costheta)/(sintheta)` `=sin^(-1)(costheta)+tan^(-1)("tan"(1)/(2)theta)` `=sin^(-1)[sin((1)/(2)pi-theta)]+tan^(-1)("tan"(1)/(2)theta)` `=(pi)/(2)-theta+(theta)/(2)=(pi)/(2)-(pi)/(2)-(1)/(2)tan^(-1)x` `(dy)/(dx)=-(1)/(2(1+x^(2)))` |
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