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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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