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why tanx/2.cotx/2 is not equal to 1 when x= 0 and if equal then see my attached image

why tanx/2.cotx/2 is not equal to 1 when x= 0 and if equal then see my attached image

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Grade:12th pass

2 Answers

Aditya Gupta
2081 Points
4 years ago
first of all your ques is wrong. we have to find tanx/2.coty/2 and not tanx/2.cotx/2. you can apply componendo and dividendo, and then use the formula (1 – cosz)/(1+cosz)= tan^2(z/2). thence you will obtain the answer root3.
now coming to why your method is wrong.
when x=0, obviously x/2 is also zero.
so tan(x/2) is also zero.
but cotx/2 is not defined at x/2=0
because it becomes infinity which is not a real number.
it is because cot(theta)= cos(theta)/sin(theta), and when theta is zero, sintheta is also zero and division by zero is not allowed (or defined).
kindly approve :)
Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
Dear student

Kindly upload complete question, otherwise tan a *cot a = 1 always except 0 and 90 degrees

Regards

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