Prove that- 1-cos -sin 2 -sin -1- cos - cot -

1+cos θ sin ^2 θ/sin θ(1+ cos θ) = sin^2 θ +cos^2 θ + cos θ sin^2 θ/sin θ(1+ cos θ) = cos θ (cos θ + 1)/sin θ(1+ cos θ) =cos θ/sin θ = cot θ ...

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Trigonometric Identities

Prove that: 1...

Question

Prove that:

$\frac{1 + c o s θ - s i n^{2} θ}{s i n θ (1 + c o s θ)} = c o t θ$

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Prove the following trigonometric identities:

$\frac{1 + c o s θ - s i n^{2} θ}{s i n θ (1 + c o s θ)} = c o t θ$

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

θ = π / 3

sin θ (1 + cos θ)

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

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