Simplify. tan x csc x

Understand Trigonometric Identities: Understand the trigonometric identities involved. The tangent function (tan x) is equal to the ratio of the sine function (sin x) to the cosine function (cos x), and the cosecant function (csc x) is the reciprocal of the sine function (sin x). So we have: tan x = sin x / cos x csc x = 1 / sin xMultiply tan x by csc x: Multiply tan x by csc x using the identities from Step 1. tan x * csc x = (sin x / cos x) * (1 / sin x)Simplify Expression: Simplify the expression by canceling out common factors. The sin x in the numerator and the sin x in the denominator cancel each other out, leaving us with: (sin x / cos x) * (1 / sin x) = 1 / cos xRecognize Secant Function: Recognize that 1 / cos x is another trigonometric identity. 1 / cos x is the secant function (sec x). Therefore, the simplified form of tan x csc x is: 1 / cos x = sec x

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Simplify. $\newline$ $\tan x \cdot \csc x$

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Algebra 1

Simplify radical expressions: mixed review

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Q. Simplify.

\newline

\tan x \cdot \csc x

Understand Trigonometric Identities: Understand the trigonometric identities involved. $\newline$ The tangent function ( $\tan x$ ) is equal to the ratio of the sine function ( $\sin x$ ) to the cosine function ( $\cos x$ ), and the cosecant function ( $\csc x$ ) is the reciprocal of the sine function ( $\sin x$ ). So we have: $\newline$ $\tan x = \frac{\sin x}{\cos x}$ $\newline$ $\csc x = \frac{1}{\sin x}$
Multiply $\tan x$ by $\csc x$ : Multiply $\tan x$ by $\csc x$ using the identities from Step $1$ . $\newline$ $\tan x \cdot \csc x = \left(\frac{\sin x}{\cos x}\right) \cdot \left(\frac{1}{\sin x}\right)$
Simplify Expression: Simplify the expression by canceling out common factors. $\newline$ The $\sin x$ in the numerator and the $\sin x$ in the denominator cancel each other out, leaving us with: $\newline$ $(\sin x / \cos x) * (1 / \sin x) = 1 / \cos x$
Recognize Secant Function: Recognize that $\frac{1}{\cos x}$ is another trigonometric identity. $\newline$ $\frac{1}{\cos x}$ is the secant function ( $\sec x$ ). Therefore, the simplified form of $\tan x \csc x$ is: $\newline$ $\frac{1}{\cos x} = \sec x$