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Factor the expression and use the fundamental identities to simplify. There is more than one...

Question:

Factor the expression and use the fundamental identities to simplify. There is more than one correct form of the answer.

{eq}6 \cos^2 x + 6 \cos^2 x \tan^2 x {/eq}

Using Trigonometric Identities:

A given expression that includes trigonometric functions of a variable (say {eq}x {/eq}), we may be able to simplify the expression using algebraic manipulation and the appropriate trigonometric identities like {eq}\sec^2 x =\tan^2 x+1 {/eq} and {eq}\sec x =\dfrac {1}{\cos x} {/eq}.

Answer and Explanation: 1

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{eq}\begin{align*} &6 \cos^2 x + 6 \cos^2 x \tan^2 x\\[2ex] = &6 \cos^2 x (1+\tan^2 x)&(\text{Factoring }6 \cos^2 x\text{ out of the expression...

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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.


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