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

Multiply and Simplify: Now, let's multiply tan(theta) by cot^2(theta) using the definitions we've just recalled: tan(theta) * cot^2(theta) = (sin(theta) / cos(theta)) * (cos^2(theta) / sin^2(theta))Cancel Common Terms: Next, we simplify the expression by canceling out common terms: (sin(theta) / cos(theta)) * (cos^2(theta) / sin^2(theta)) = sin(theta) * cos(theta) / sin^2(theta) Here, cos(theta) in the numerator and one sin(theta) in the denominator cancel out: = cos(theta) / sin(theta)Use Definition of cot(theta): The expression cos(theta) / sin(theta) is the definition of cot(theta): cos(theta) / sin(theta) = cot(theta) So, the simplified expression is cot(theta).

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Simplify to a single trig function with no denominator.

tan theta*cot^(2)theta
Answer:

theta

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

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

\newline

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

\newline

Answer:

Multiply and Simplify: Now, let's multiply $\tan(\theta)$ by $\cot^2(\theta)$ using the definitions we've just recalled: $\newline$ $\tan(\theta) \cdot \cot^2(\theta) = (\sin(\theta) / \cos(\theta)) \cdot (\cos^2(\theta) / \sin^2(\theta))$
Cancel Common Terms: Next, we simplify the expression by canceling out common terms: $\newline$ $(\sin(\theta) / \cos(\theta)) \cdot (\cos^2(\theta) / \sin^2(\theta)) = \sin(\theta) \cdot \cos(\theta) / \sin^2(\theta)$ $\newline$ Here, $\cos(\theta)$ in the numerator and one $\sin(\theta)$ in the denominator cancel out: $\newline$ $= \cos(\theta) / \sin(\theta)$
Use Definition of cot(theta): The expression $\frac{\cos(\theta)}{\sin(\theta)}$ is the definition of $\cot(\theta)$ : $\frac{\cos(\theta)}{\sin(\theta)} = \cot(\theta)$ So, the simplified expression is $\cot(\theta)$ .