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

Express cot(theta): Express cot(theta) in terms of sin(theta) and cos(theta) as cot(theta) = cos(theta)/sin(theta).Substitute cot(theta): Substitute cot(theta) with cos(theta)/sin(theta) in the given expression to get sin^(2)theta * (cos(theta)/sin(theta))^(2).Simplify the expression: Simplify the expression by squaring the cot(theta) term to get sin^(2)theta * (cos^(2)theta/sin^(2)theta).Cancel out terms: Cancel out the sin^(2)theta in the numerator with one of the sin^(2)theta in the denominator to get cos^(2)theta.Recognize simplified form: Recognize that cos^(2)theta is already a single trigonometric function with no denominator, which is the simplified form of the original expression.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify to a single trig function with no denominator.

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

theta

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

View step-by-step help

Home

Math Problems

Algebra 2

Simplify expressions using trigonometric identities

Full solution

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

\newline

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

\newline

Answer:

Express $\cot(\theta)$ : Express $\cot(\theta)$ in terms of $\sin(\theta)$ and $\cos(\theta)$ as $\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}$ .
Substitute $\cot(\theta)$ : Substitute $\cot(\theta)$ with $\frac{\cos(\theta)}{\sin(\theta)}$ in the given expression to get $\sin^{2}\theta \cdot \left(\frac{\cos(\theta)}{\sin(\theta)}\right)^{2}$ .
Simplify the expression: Simplify the expression by squaring the $\cot(\theta)$ term to get $\sin^{2}\theta \times (\cos^{2}\theta/\sin^{2}\theta)$ .
Cancel out terms: Cancel out the $\sin^{2}\theta$ in the numerator with one of the $\sin^{2}\theta$ in the denominator to get $\cos^{2}\theta$ .
Recognize simplified form: Recognize that $\cos^2(\theta)$ is already a single trigonometric function with no denominator, which is the simplified form of the original expression.