Evaluate the integral: \int^{\frac{2 \pi}{3}}_0 \frac{7 \sin \theta + 7 \sin \theta \tan^2...

Question:

Evaluate the integral: {eq}\int^{\frac{2 \pi}{3}}_0 \frac{7 \sin \theta + 7 \sin \theta \tan^2 \theta}{\sec^2 \theta }d \theta{/eq}

Trigonometric Pythagorean Identities:

There are several trigonometric identities that are utilized frequently in trigonometry and calculus. These identities are known as the Pythagorean identities and are:

{eq}\sin^{2}\theta+\cos^{2}\theta=1\hspace{10mm}\tan^{2}\theta+1=\sec^{2}\theta\hspace{10mm}1+\cot^{2}\theta=\csc^{2}\theta {/eq}

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Step 1. Factor the numerator of the integrand.

{eq}\int^{\frac{2 \pi}{3}}_0 \frac{7 \sin \theta + 7 \sin \theta \tan^2 \theta}{\sec^2 \theta }d... Trigonometric Identities: Definition & Uses

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Chapter 23 / Lesson 1
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Trigonometric identities are equations that are always true for trigonometric functions. Learn about the definition and kinds of trigonometric identities and explore the uses of trigonometric identities through examples.