InterviewSolution
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InterviewSolution
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सिद्ध कीजिए कि `2 tan^(-1)""(1)/(x)=sin^(-1)""((2x)/(x^(2)+1))` |
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Answer» माना `tan^(-1)""(1)/(x)=thetaimplies (1)/(x)=tan theta implies cot theta =x` `:.` बायाँ पक्ष `=2tan^(-1)""(1)/(x)=2 theta ` अब , दायाँ पक्ष `=sin^(-1)((2x)/(x^(2)+1))` `=sin^(-1)((2cot theta)/(1+cot^(2)theta))=sin^(-1)((2 tan theta )/(1+tan^(2)theta))` `= sin^(-1)(sin2 theta)=2 theta=2tan^(-1)""(1)/(x)` `implies sin^(-1)((2x)/(x^(2)+1))=2tan^(-1)""(1)/(x)` |
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