1 + sin A / 1-sin A + 1- sin A/ 1+ sin A = sec ²A+tan²A​

Question

1 + sin A / 1-sin A + 1- sin A/ 1+ sin A = sec ²A+tan²A​

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Vivian 4 weeks 2021-08-18T23:55:09+00:00 1 Answer 0 views 0

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    2021-08-18T23:56:12+00:00

    L.H.S. = √{(1 – sina)/(1 + sina)}

    = √[{(1 – sina)(1 – sina)}/{(1 + sina)(1 – sina)}]

    = √{(1 – sina)²/(1 – sin²a)}

    = √{(1 – sina)²/cos²a}

    = √{(1 – sina)/cosa}²

    = (1 – sina)/cosa

    = 1/cosa – sina/cosa

    = seca – tana = R.H.S.

    Hence proved.

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