InterviewSolution
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InterviewSolution
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Prove that: i) `tan^(-1)(sqrt(x)+sqrt(y))/(1-sqrt(xy))=tan^(-1)sqrt(x)+tan^(-1)sqrt(y)` ii) `tan^(-1)(x+sqrt(x))/(1-x^(3//2))=tan^(-1)x+tan^(-1)sqrt(x)` iii) `tan^(-1)(sinx)/(1+cosx)=x/2` |
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Answer» i) Put `sqrt(x)=tantheta` and `sqrt(y)=tanphi` on each side. ii) Put `x=tantheta` and `sqrt(x)=tanphi` on each side. iii) LHS `=tan^(-1){(2sin(x/2)cos(x/2))/(2cos^(2)x/2)}=tan^(-1)(tanx/2)=x/2`= RHS |
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