Chapter 7: Q. 30 (page 503)

In Problems 28 – 44, establish each identity.
$5 \cos^{2} θ + 3 \sin^{2} θ = 3 + 2 \cos^{2} θ$

Short Answer

Expert verified

The given identity is established.

Step by step solution

Step 1. Given Information

The given expression is $5 \cos^{2} θ + 3 \sin^{2} θ = 3 + 2 \cos^{2} θ .$

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.

L.H.S

$5 \cos^{2} θ + 3 \sin^{2} θ = 2 \cos^{2} θ + 3 \cos^{2} θ + 3 \sin^{2} θ = 2 \cos^{2} θ + 3 (\cos^{2} θ + \sin^{2} θ) [\sin^{2} θ + \cos^{2} θ = 1] = 2 \cos^{2} θ + 3$

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

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In Problems 28 – 44, establish each identity.
$5 \cos^{2} θ + 3 \sin^{2} θ = 3 + 2 \cos^{2} θ$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Establishing the identity

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In Problems 28 – 44, establish each identity.5cos2θ+3sin2θ=3+2cos2θ

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

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

In Problems 28 – 44, establish each identity.
$5 \cos^{2} θ + 3 \sin^{2} θ = 3 + 2 \cos^{2} θ$