InterviewSolution
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InterviewSolution
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सिद्ध कीजिए कि ` tan^(-1)((x)/(sqrt(a^(2)-x^(2))))=sin^(-1)""(x)/(a)` |
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Answer» हमें सिद्ध करना है कि ` tan^(-1)((x)/(sqrt(a^(2)-x^(2))))=sin^(-1)""(x)/(a)` माना `sin^(0-1)""(x)/(a)=theta` तब `(x)/(a)=sin thetaimpliesx=a sin theta` ` :. (x)/(sqrt(a^(2)-x^(2)))=(a sin theta)/(sqrt(a^(2)-x^(2)sin^(2)theta))` `= (a sin theta)/(a cos theta)=tan theta ` `implies tan^(-1)((x)/(sqrt(a^(2)-x^(2))))= tan^(-1)(tan theta)=theta` तथा `theta=sin^(-1)""(x)/(a)` `implies tan^(-1)((x)/(sqrt(a^(2)-x^(2))))=sin^(-1)""(x)/(a)` |
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