Chapter 7: Q. 14 (page 505)

Establish the identity
$\frac{\sin (α + β)}{\tan α + \tan β} = \cos α \cos β$

Short Answer

Expert verified

By applying the sum formula of sin function we get $\frac{\sin (α + β)}{\tan α + \tan β} = \cos α \cos β$

Step by step solution

Step 1. Given information

$\frac{\sin (α + β)}{\tan α + \tan β} = \cos α \cos β$

Step 2. Calculations

$\frac{\sin (α + β)}{\tan α + \tan β} = \cos α \cos β$

take LHS, $\frac{\sin (α + β)}{\tan α + \tan β}$

$\sin (α + β) = \sin α \cos β + \cos α \sin β \tan α + \tan β = \frac{\sin α}{\cos α} + \frac{\sin β}{\cos β} = \frac{\sin α \cos β + \cos α \sin β}{\cos α \cos β} \frac{\sin (α + β)}{\tan α + \tan β} = \frac{\sin α \cos β + \cos α \sin β}{\frac{\sin α \cos β + \cos α \sin β}{\cos α \cos β}} = \cos α \cos β$

LHS=RHS

Hence identity is established.

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Establish the identity
$\frac{\sin (α + β)}{\tan α + \tan β} = \cos α \cos β$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculations

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Establish the identity sin(α+β)tanα+tanβ=cosαcosβ

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Establish the identity
$\frac{\sin (α + β)}{\tan α + \tan β} = \cos α \cos β$