Chapter 7: Q. 40 (page 474)

In problems 19-98, establish each identity.
$9 \sec^{2} (θ) - 5 \tan^{2} (θ) = 5 + 4 \sec^{2} (θ)$

Short Answer

Expert verified

We have proved the identity $9 \sec^{2} (θ) - 5 \tan^{2} (θ) = 5 + 4 \sec^{2} (θ)$ .

Step by step solution

Step 1. Given information.

We have:

$9 \sec^{2} (θ) - 5 \tan^{2} (θ) = 5 + 4 \sec^{2} (θ)$

Step 2. Establish the identity.

Take the left hand side:

$9 \sec^{2} (θ) - 5 \tan^{2} (θ)$

Apply identity: role="math" localid="1646583478228" $\tan^{2} θ = \sec^{2} (θ) - 1$
$= 9 \sec^{2} (θ) - 5 (s e c^{2} θ - 1) = 9 \sec^{2} (θ) - 5 s e c^{2} θ + 5 = 5 + 4 s e c^{2} (θ)$

Hence, proved.

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In problems 19-98, establish each identity.
$9 \sec^{2} (θ) - 5 \tan^{2} (θ) = 5 + 4 \sec^{2} (θ)$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Establish the identity.

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In problems 19-98, establish each identity.9sec2θ-5tan2θ=5+4sec2θ

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Establish the identity.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Calculus

Mechanics Maths

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

In problems 19-98, establish each identity.
$9 \sec^{2} (θ) - 5 \tan^{2} (θ) = 5 + 4 \sec^{2} (θ)$