Chapter 7: Q. 86 (page 475)

Establish each identity.
$\frac{1 - 2 \cos^{2} θ}{\sin θ \cos θ} = \tan θ - c o t θ$

Short Answer

Expert verified

The right side of the given equation has been simplified to bring the left side.

Step by step solution

Step 1. Given Information

The given equation is $\frac{1 - 2 \cos^{2} θ}{\sin θ \cos θ} = \tan θ - c o t θ$

Step 2. Calculation

Consider the right side of the given equation and simplify to bring the left side in order to establish the equation.

$\tan θ - c o t θ = \frac{\sin θ}{\cos θ} - \frac{\cos θ}{\sin θ} = \frac{\sin^{2} θ - \cos^{2} θ}{\sin θ \cos θ} = \frac{1 - \cos^{2} θ - \cos^{2} θ}{\sin θ \cos θ} = \frac{1 - 2 \cos^{2} θ}{\sin θ \cos θ}$

Hence, Proved

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Establish each identity.
$\frac{1 - 2 \cos^{2} θ}{\sin θ \cos θ} = \tan θ - c o t θ$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

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Establish each identity.1-2cos2θsinθcosθ=tanθ-cotθ

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

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Study anywhere. Anytime. Across all devices.

Establish each identity.
$\frac{1 - 2 \cos^{2} θ}{\sin θ \cos θ} = \tan θ - c o t θ$