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Chapter 5: Problem 39

Use the fundamental identities to simplify the expression. There is more than one correct form of each answer. $$\tan (-x) \cos x$$

Short Answer

Expert verified
The simplified form of the expression \( \tan (-x) \cos x \) is \( -\sin x \)

Step by step solution

01

Apply the properties of Tan

We know that \( \tan(-x) = -\tan x \) by the definition of the tangent of a negative angle.
02

Express Tan in terms of Sine and Cosine

Using one of the quotient identities, \( \tan x = \sin x / \cos x \), we can replace \( \tan x \) in our expression. That would make the new expression : \( -\sin x * \cos x / \cos x \).
03

Simplify the expression

The \( \cos x \) in the numerator and denominator will cancel out, hence the simplified expression is \( -\sin x \)

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