InterviewSolution
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InterviewSolution
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`tan(1/2cos^(- 1) sqrt(5)/3)`A. `(3-sqrt(5))/(2)`B. `(3+sqrt(5))/(2)`C. `(5-sqrt(3))/(2)`D. `(5+sqrt(3))/(2)` |
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Answer» Correct Answer - A Let `cos^(-1)sqrt(5)/3=theta`. Then, `costheta =sqrt(5)/3`. `tan1/2(cos^(-1)sqrt(5)/3)=tan1/2theta=(sin(theta/2))/(cos(theta/2))`. `=sqrt((1-costheta)/(1+costheta))={(1-sqrt(5)/3)/(1+sqrt(5)/3)}^(1//2)` `((3-sqrt(5))/(3+sqrt(5)))^(1//2)={(3-sqrt(5))/(3+sqrt(5)) xx (3-sqrt(5))/(3-sqrt(5))}^(1//2)=(3-sqrt(5))/(2)`. |
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