InterviewSolution
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InterviewSolution
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Prove that `2tan^(-1)1/x=sin^(-1)((2x)/(x^(2)+1))` |
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Answer» Let `tan^(-1)1/x=theta`. Then, `1/x=tantheta rArr x=cottheta`. `therefore` LHS `=2tan^(-1)1/x=2theta`. RHS `=sin^(-1)(2cottheta)/(cot^(2)theta+1)=sin^(-1)(2tantheta)/(1+tan^(2)theta)` `=sin^(-1)(sin 2theta)=2theta` `therefore` LHS=RHS. Hence, `2tan^(-1)1/x=sin^(-1)((2x)/(x^(2)+1))`. |
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