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

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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