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Prove the following identities, where the angles involved are acute angles for which the expressions are defined.(x) (1+tan2A/1+cot2A) = (1-tan A/1-cot A)2 = tan2A. Q.5(10)

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What is the best way to find the ncert class 10 question of trigonometry  in a simplest and easiest way . Please help me to find the best solution of exercise 8.4of the trigonometry . Prove the following identities, where the angles involved are acute angles for which the expressions are defined.(x) (1+tan2A/1+cot2A) = (1-tan A/1-cot A)2 = tan2A.

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  1. (1+tan2A/1+cot2A) = (1-tan A/1-cot A)2 = tan2A

    L.H.S. = (1+tan2A/1+cot2A)

    Since cot function is the inverse of tan function,

    = (1+tan2A/1+1/tan2A)

    = 1+tan2A/[(1+tan2A)/tan2A]

    Now cancel the 1+tan2A terms, we get

    = tan2A

    (1+tan2A/1+cot2A) = tan2A

    Similarly,

    (1-tan A/1-cot A)2 = tan2A

    Hence proved

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