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

Express tan and csc: Express tan(theta) and csc(theta) in terms of sin(theta) and cos(theta). tan(theta) is sin(theta)/cos(theta) and csc(theta) is 1/sin(theta).Write tan^(2) and csc^(2): Write tan^(2)theta and csc^(2)theta using the expressions from Step 1. tan^(2)theta becomes (sin(theta)/cos(theta))^2 and csc^(2)theta becomes (1/sin(theta))^2.Multiply the expressions: Multiply the expressions from Step 2. (sin(theta)/cos(theta))^2 * (1/sin(theta))^2 simplifies to (sin^2(theta)/cos^2(theta)) * (1/sin^2(theta)).Simplify the expression: Simplify the expression by canceling out sin^2(theta) in the numerator and denominator. (sin^2(theta)/cos^2(theta)) * (1/sin^2(theta)) simplifies to 1/cos^2(theta).Recognize the definition: Recognize that 1/cos^2(theta) is the definition of sec^2(theta). Therefore, the simplified expression is sec^2(theta).

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Simplify to a single trig function with no denominator.

tan^(2)theta*csc^(2)theta
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theta

Simplify to a single trig function with no denominator. $\newline$ $\tan ^{2} \theta \cdot \csc ^{2} \theta$ $\newline$ 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

\tan ^{2} \theta \cdot \csc ^{2} \theta

\newline

Answer:

Express $\tan$ and $\csc$ : Express $\tan(\theta)$ and $\csc(\theta)$ in terms of $\sin(\theta)$ and $\cos(\theta)$ . $\newline$ $\tan(\theta)$ is $\frac{\sin(\theta)}{\cos(\theta)}$ and $\csc(\theta)$ is $\frac{1}{\sin(\theta)}$ .
Write $\tan^2$ and $\csc^2$ : Write $\tan^2\theta$ and $\csc^2\theta$ using the expressions from Step $1$ . $\newline$ $\tan^2\theta$ becomes $(\sin(\theta)/\cos(\theta))^2$ and $\csc^2\theta$ becomes $(1/\sin(\theta))^2$ .
Multiply the expressions: Multiply the expressions from Step $2$ . $\newline$ $(\frac{\sin(\theta)}{\cos(\theta)})^2 \times (\frac{1}{\sin(\theta)})^2$ simplifies to $(\frac{\sin^2(\theta)}{\cos^2(\theta)}) \times (\frac{1}{\sin^2(\theta)})$ .
Simplify the expression: Simplify the expression by canceling out $\sin^2(\theta)$ in the numerator and denominator. $\frac{\sin^2(\theta)}{\cos^2(\theta)} \times \frac{1}{\sin^2(\theta)}$ simplifies to $\frac{1}{\cos^2(\theta)}$ .
Recognize the definition: Recognize that $\frac{1}{\cos^2(\theta)}$ is the definition of $\sec^2(\theta)$ . Therefore, the simplified expression is $\sec^2(\theta)$ .