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If cot( A+B).cot(A-B) = 1, then the value of cot (2A/3) is:
Question

If cot( A+B).cot(A-B) = 1, then the value of cot (2A/3) is:

A.

32\frac{\sqrt3}{2}​​

B.

23\frac{\sqrt2}{3}​​

C.

13\frac{1}{\sqrt3}​​

D.

3\sqrt3​​

Correct option is D

Given:

cot( A+B).cot(A-B) = 1

Value Used:

Cot(45°\degree​) =1

Solution:

Let value of B = 0 

cot( A+B).cot(A-B) = 1

Put the value of B in equation 

cot( A+0).cot(A-0) = 1

(cot(A))2^2 =1

Cot(A)=Cot(45°\degree​​)

A =45°\degree 

So, Value of cot (2A/3) = cot (90/3)

Cot(30)= 3\sqrt3​ 

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