Evaluate:`tan{1/2cos^(-1)(sqrt5/3)}`

1.	Evaluate:`tan{1/2cos^(-1)(sqrt5/3)}`
Answer» `tan[ 1/2 cos^-1(sqrt5/3)]` `1/2 cos^-1(sqrt5/3) = theta` `cos^-1(sqrt5/3) = 2 theta` `cos 2theta = sqrt5/3` `(1- tan^2 theta)/(1 + tan^2 theta) = sqrt5/3` `3- 3 tan^2 theta = sqrt5 + sqrt5 tan^2 theta` `sqrt((3 - sqrt5)/(3 + sqrt5))= tan theta` `sqrt(((3- sqrt5)(3- sqrt5))/((3 + sqrt5)(3- sqrt5))) = tan theta` `tan theta = sqrt((3- sqrt5)^2/4)` `= (3- sqrt5)/2` Answer

Discussion

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