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

Understand Trigonometric Identities: Understand the trigonometric identities involved. The cosecant function is the reciprocal of the sine function, so csc(theta) = 1/sin(theta). Therefore, csc^(2)(theta) = 1/sin^(2)(theta).Multiply by sin^(2)(theta): Multiply csc^(2)(theta) by sin^(2)(theta). Since csc^(2)(theta) = 1/sin^(2)(theta), we have: csc^(2)(theta) * sin^(2)(theta) = (1/sin^(2)(theta)) * sin^(2)(theta).Simplify the Expression: Simplify the expression. The sin^(2)(theta) in the numerator and denominator cancel each other out, leaving us with: (1/sin^(2)(theta)) * sin^(2)(theta) = 1.

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Simplify to a single trig function with no denominator.

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

theta

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

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Algebra 2

Simplify radical expressions with variables II

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

\newline

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

\newline

Answer:

Understand Trigonometric Identities: Understand the trigonometric identities involved. $\newline$ The cosecant function is the reciprocal of the sine function, so $\csc(\theta) = \frac{1}{\sin(\theta)}$ . Therefore, $\csc^{2}(\theta) = \frac{1}{\sin^{2}(\theta)}$ .
Multiply by $\sin^{2}(\theta)$ : Multiply $\csc^{2}(\theta)$ by $\sin^{2}(\theta)$ . Since $\csc^{2}(\theta) = \frac{1}{\sin^{2}(\theta)}$ , we have: $\csc^{2}(\theta) \times \sin^{2}(\theta) = \left(\frac{1}{\sin^{2}(\theta)}\right) \times \sin^{2}(\theta)$ .
Simplify the Expression: Simplify the expression. $\newline$ The $\sin^{2}(\theta)$ in the numerator and denominator cancel each other out, leaving us with: $\newline$ $\frac{1}{\sin^{2}(\theta)} \times \sin^{2}(\theta) = 1$ .