1+cos theta +sin theta /1+cos theta - sin theta =1+sin theta /cos theta. Prove the above .

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Prove the following trigonometric identities.
(i) $\frac{1 + cos θ + sin θ}{1 + cos θ - sin θ} = \frac{1 + sin θ}{cos θ}$

(ii) $\frac{sin θ - cos θ + 1}{sin θ + cos θ - 1} = \frac{1}{sec θ - tan θ}$

(iii) $\frac{cos θ - sin θ + 1}{cos θ + sin θ - 1} = cosec θ + cot θ$

(iv) $(sin θ + cos θ) (tan θ + cot θ) = sec θ + cosec θ$

\frac{1 + sin θ}{cos θ} = \frac{sin θ - cos θ + {sin}^{2} θ + {cos}^{2} θ}{sin θ + cos θ - 1}

Prove that:

tan theta - cot theta = 2sin²theta - 1/sin theta cos theta = 1-2cos²theta /sin theta cos theta

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