Chapter 7: Q. 59 (page 486)

In Problems 47–72, establish each identity.
$\frac{\sin (α + β)}{\sin α \cos β} = 1 + c o t α \tan β$

Short Answer

Expert verified

The given identity is established.

Step by step solution

Step 1. Given Information

The given expression is $\frac{\sin (α + β)}{\sin α \cos β} = 1 + c o t α \tan β$

We have to establish each identity.

Step 2. Establishing the identity

We can establish the given expression as an identity by simplifying one side to give the other side.

So, use the sum identity for the sine function, $\sin (α + β) = \sin α \cos β + \cos α \sin β .$

L.H.S

$\frac{\sin (α + β)}{\sin α \cos β} = \frac{\sin α \cos β + \cos α \sin β}{\sin α \cos β} = \frac{\sin α \cos β}{\sin α \cos β} + \frac{\cos α \sin β}{\sin α \cos β} = 1 + c o t α \tan β$

Thus, L.H.S = R.H.S and the given expression is an identity.

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In Problems 47–72, establish each identity.
$\frac{\sin (α + β)}{\sin α \cos β} = 1 + c o t α \tan β$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Establishing the identity

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In Problems 47–72, establish each identity.sinα+βsinαcosβ=1+cotαtanβ

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Establishing the identity

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Pure Maths

Applied Mathematics

Decision Maths

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In Problems 47–72, establish each identity.
$\frac{\sin (α + β)}{\sin α \cos β} = 1 + c o t α \tan β$