Chapter 7: Q. 12 (page 505)

Establish the identity
$\sin θ \tan θ + \cos θ = s e c θ$

Short Answer

Expert verified

$B y w r i t n g \tan θ = \frac{\sin θ}{\cos θ} w e g e t \sin θ \tan θ + \cos θ = s e c θ$

Step by step solution

Step 1. Given information

$\sin θ \tan θ + \cos θ = s e c θ$

Step 2. Calculations

$\sin θ \tan θ + \cos θ = s e c θ T a k e L H S \sin θ \tan θ + \cos θ W e k n o w t h a t \tan θ = \frac{\sin θ}{\cos θ} S o, \sin θ \tan θ + \cos θ = \sin θ \frac{\sin θ}{\cos θ} + \cos θ = \frac{\sin^{2} θ + \cos^{2} θ}{\cos θ} = \frac{1}{\cos θ} = s e c θ H e n c e L H S = R H S$

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Establish the identity
$\sin θ \tan θ + \cos θ = s e c θ$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculations

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Establish the identity
$\sin θ \tan θ + \cos θ = s e c θ$