First slide

Trigonometric Identities

Question

$\frac{\tan θ + \sec θ - 1}{\tan θ - \sec θ + 1} =$

Moderate

A

$\frac{1 - \cos θ}{\sin θ}$
B

$\frac{1 - \sin θ}{\cos θ}$
C

$\frac{1 + \cos θ}{\sin θ}$
D

$\frac{1 + \sin θ}{\cos θ}$

Solution

$\frac{\tan θ + \sec θ - 1}{\tan θ - \sec θ + 1} =$ $\frac{\tan θ + \sec θ - (\sec^{2} θ - \tan^{2} θ)}{\tan θ - \sec θ + 1}$
                                 $= \frac{(\tan θ + \sec θ) (1 - \sec θ + \tan θ)}{\tan θ - \sec θ + 1}$

                                 $= \tan θ + \sec θ$

                                 $= \frac{1 + \sin θ}{\cos θ}$

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