Question

In Exercises $15-20,$ write each expression in terms of $\sin x$ and/or $\cos x$ only. $$\sec x \cot x$$

   In Exercises $15-20,$ write each expression in terms of $\sin x$ and/or $\cos x$ only.
$$\sec x \cot x$$

Precalculus : Building Concepts and Connections

Precalculus : Building Concepts and Connections

Revathi Narasimhan 1st Edition

Chapter 6, Problem 18

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Solved by Expert Joshua Eastwood

04/11/2020

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We know that $\sec x$ is equivalent to $\frac{1}{\cos x}$ and $\cot x$ is equivalent to $\frac{\cos x}{\sin x}$. Show more…

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In Exercises $15-20,$ write each expression in terms of $\sin x$ and/or $\cos x$ only. $$\sec x \cot x$$

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Key Concepts

Simplification of Trigonometric Expressions

Simplification involves applying various trigonometric identities and algebraic manipulations to reduce expressions to their simplest form. This can include canceling common factors or substituting equivalent expressions, thereby making the expression more straightforward to work with in further calculations.

Expressing Functions in Terms of Sine and Cosine

This concept involves rewriting different trigonometric expressions solely in terms of sine and cosine. It is particularly useful because sine and cosine are the most fundamental trigonometric functions, making it easier to simplify, differentiate, or integrate expressions once all terms are written in these base functions.

Reciprocal Identities

Reciprocal identities allow trigonometric functions to be expressed as the reciprocal of other functions. For instance, the secant function is the reciprocal of the cosine function. This concept facilitates rewriting terms by substituting these reciprocal relationships.

Quotient Identities

Quotient identities express one trigonometric function as the ratio of two others. A prime example is the cotangent function, which is defined as the quotient of the cosine function by the sine function. This relationship helps in converting and simplifying expressions.

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