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1 April, 17:39

Prove that, 1+sin t/cos t = cos t/1-sin t

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  1. 1 April, 17:48
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    Given:

    1 + sin t/cos t = cos t / 1 - sin t

    We will first multiply the numerator and denominator of the left side of the identity by the expression (1 - sin t)

    (1 + sin t) · (1 - sin t) / cost · (1 - sin t) = 1 - sin² t / cos t · (1 - sin t)

    We know it is sin² t + cos² t = 1 = > cos² t = 1 - sin² t

    if we replace 1 - sin² t with cos² t that we get

    cos² t / cos t · (1 - sin t) = cos t / 1 - sin t the proof is complete.

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