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    Mathematics - Trigonometry - Identities

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    Prove the following Identities:

    Prove the following Identities:

    1. tan² A / sec² A = 1 - cot ² A / csc² a

    2. 1 / 1 - cos A tan A = cot A / cot A - cos A

    3. cos² A ( 1 - sec² A) / cot² A sin² A - 1 = 1

    4. (cot A = tan A) ² = sec² B csc² B°

    Where A + B = 90°

    © BrainMass Inc. brainmass.com October 9, 2019, 9:55 pm ad1c9bdddf
    https://brainmass.com/math/trigonometry/mathematics-trigonometry-identities-201931

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    (1) LHS = tan^2 A / sec^2 A = (sin^2 A / cos^2 A) / (1 / cos^2 A) = sin^2 A
    RHS = 1 - cot^2 A / csc^2 A = 1 - [(cos^2 A / sin^2 A) / (1 / sin^2 A)] = 1 - cos^2 A = sin^2 A
    LHS = RHS

    (2) LHS ...

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