Prove that : 2 tan^-1 (2x/1 - x^2) = 2 pi/3
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Answer :
2 tan^-1 (2x/1 - x^2) = 2 pi/3
Take x as tan theta
Theta = tan^-1 x
tan^-1(2 tan theta/ 1 - tan^2 theta) = pi/3
tan^-1 (tan 2 theta) = pi/3
2 theta = pi/3
theta = pi/6
tan^-1 x = pi/6
x = tan pi/6
x = 1/root 3
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2 tan^-1 (2x/1 - x^2) = 2 pi/3
Take x as tan theta
Theta = tan^-1 x
tan^-1(2 tan theta/ 1 - tan^2 theta) = pi/3
tan^-1 (tan 2 theta) = pi/3
2 theta = pi/3
theta = pi/6
tan^-1 x = pi/6
x = tan pi/6
x = 1/root 3
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