InterviewSolution
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InterviewSolution
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Prove that `tan^(-1)(x/sqrt(a^(2)-x^(2)))=sin^(-1)x/a.` |
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Answer» Putting, `x=asintheta`, we get LHS`=tan^(-1)(x/sqrt(a^(2)+x^(2))` `=tan^(-1)(asintheta)/sqrt(a^(2)-a^(2)sin^(2)theta)`. `=tan^(-1)(asintheta)/(a costheta)=tan^(-1)(tantheta)` `=theta=sin^(-1)x/a`=RHS. `therefore tan^(-1)(1/(sqrt(x^(2)-1))=(pi/2-sec^(-1)x)`. |
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