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1 November, 10:55

1+sin (a) / 1+csc (a) = tan (a) / sec (a)

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  1. 1 November, 11:02
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    Below.

    Step-by-step explanation:

    (1 + sin a) / (1 + csc a)

    = (1 + sin a) / (1 + 1 / sin a)

    = (1 + sin a) / (sin a + 1) / (sin a)

    = (sin a (1 + sin a)) / (1 + sin a)

    = sin a.

    tan a / sec a

    = (sin a / cos a) / (1 / cos a)

    = (sin a cos a) / cos a

    = sin a

    The two expressions are both equal to sin a:

    Therefore

    (1 + sin a) / (1 + csc a) = tan a / sec a.
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