Simplify to a single trig function with no denominator. sin^(2)theta*sec^(2)theta Answer: theta

Express sec(theta): Express sec(theta) in terms of cos(theta) as sec(theta) = 1/cos(theta).Substitute and simplify: Substitute sec(theta) with 1/cos(theta) in the given expression to get sin^(2)theta*(1/cos(theta))^2.Recognize equivalent form: Simplify sin^(2)theta*(1/cos(theta))^2 as sin^(2)theta*cos^(-2)theta.Rewrite as tan(theta): Recognize that sin^(2)theta*cos^(-2)theta is equivalent to (sin(theta)/cos(theta))^2.Conclude final result: Recall that sin(theta)/cos(theta) is the definition of tan(theta), so we can rewrite the expression as tan^(2)theta.Conclude that sin^(2)theta*sec^(2)theta simplifies to tan^(2)theta.

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Simplify to a single trig function with no denominator.

sin^(2)theta*sec^(2)theta
Answer:

theta

Simplify to a single trig function with no denominator. $\newline$ $\sin ^{2} \theta \cdot \sec ^{2} \theta$ $\newline$ Answer:

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Algebra 2

Simplify expressions using trigonometric identities

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Q. Simplify to a single trig function with no denominator.

\newline

\sin ^{2} \theta \cdot \sec ^{2} \theta

\newline

Answer:

Express $\sec(\theta)$ : Express $\sec(\theta)$ in terms of $\cos(\theta)$ as $\sec(\theta) = \frac{1}{\cos(\theta)}$ .
Substitute and simplify: Substitute $\sec(\theta)$ with $\frac{1}{\cos(\theta)}$ in the given expression to get $\sin^{2}\theta\left(\frac{1}{\cos(\theta)}\right)^2$ .
Recognize equivalent form: Simplify $\sin^{2}\theta\left(\frac{1}{\cos(\theta)}\right)^2$ as $\sin^{2}\theta\cos^{-2}\theta$ .
Rewrite as $\tan(\theta)$ : Recognize that $\sin^{2}\theta\cos^{-2}\theta$ is equivalent to $\left(\frac{\sin(\theta)}{\cos(\theta)}\right)^2$ .
Conclude final result: Recall that $\sin(\theta)/\cos(\theta)$ is the definition of $\tan(\theta)$ , so we can rewrite the expression as $\tan^{2}\theta$ .
Conclude final result: Recall that $\sin(\theta)/\cos(\theta)$ is the definition of $\tan(\theta)$ , so we can rewrite the expression as $\tan^{2}\theta$ .Conclude that $\sin^{2}\theta \cdot \sec^{2}\theta$ simplifies to $\tan^{2}\theta$ .