First slide

Trigonometric Identities

Question

$\frac{\cot θ + \cos e c θ - 1}{\cot θ - \cos e c θ + 1} =$

Moderate

A

$\frac{\sin θ}{1 + \cos θ}$
B

$\frac{\sin θ}{1 - \cos θ}$
C

$\frac{1 - \cos θ}{\sin θ}$
D

$\frac{\cos θ}{1 - \sin θ}$

Solution

$1 = \cos e c^{2} θ - \cot^{2} θ \Rightarrow \cos e c θ - co t θ = \frac{1}{\cos e c θ + \cot θ} ∴ \frac{\cot θ + \cos e c θ - 1}{\cot θ - \cos e c θ + 1} = \cos e c θ + c o t θ = \frac{1 + \cos θ}{\sin θ} = \frac{\sin θ}{1 - \cos θ}$

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