Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify to a single trig function with no denominator.

(tan^(2)theta)/(sec^(2)theta)
Answer:

theta

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

View step-by-step help

View step-by-step help

Simplify expressions using trigonometric identities

Full solution

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

\newline

\frac{\tan ^{2} \theta}{\sec ^{2} \theta}

\newline

Answer:

Express tan and sec: Express $\tan(\theta)$ and $\sec(\theta)$ in terms of sine and cosine. $\newline$ $\tan(\theta)$ is the ratio of $\sin(\theta)$ to $\cos(\theta)$ , so $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$ . $\newline$ $\sec(\theta)$ is the reciprocal of $\cos(\theta)$ , so $\sec(\theta) = \frac{1}{\cos(\theta)}$ .
Write $\tan^2\theta$ : Write $\tan^2\theta$ and $\sec^2\theta$ using the expressions from Step $1$ . $\newline$ $\tan^2\theta = \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^2$ $\newline$ $\sec^2\theta = \left(\frac{1}{\cos(\theta)}\right)^2$
Substitute expressions: Substitute the expressions from Step $2$ into the given expression. $\newline$ $\frac{\tan^{2}\theta}{\sec^{2}\theta} = \frac{(\frac{\sin(\theta)}{\cos(\theta)})^2}{(\frac{1}{\cos(\theta)})^2}$
Simplify the expression: Simplify the expression by canceling out common terms. The $\cos(\theta)$ in the denominator of $\tan^{2}(\theta)$ and the $\cos(\theta)$ in the numerator of $\sec^{2}(\theta)$ will cancel out. This leaves us with $(\sin(\theta))^2$ .
Recognize $\sin^2\theta$ : Recognize that $(\sin(\theta))^2$ is simply $\sin^2\theta$ . So, the simplified expression is $\sin^2\theta$ .

More problems from Simplify expressions using trigonometric identities

Question

\cos(\theta)=\frac{8}{17}

0^\circ<\theta<90^\circ

\sec(\theta)

? Write your answer in simplified, rationalized form.

\sec(\theta)=

Posted 2 months ago

Question

\cos(x) = -0.3

\sin(90^\circ - x)

Posted 2 months ago

Question

\csc(\theta) = \frac{17}{8}

0^\circ < \theta < 90^\circ

\tan(\theta)

\newline

Write your answer in simplified, rationalized form.

\newline

\tan(\theta) =

\newline

Posted 2 months ago

Question

Is the sine function even or odd?

\newline

\newline

\text{[A]even}

\newline

\text{[B]odd}

Posted 2 months ago

Question

Write the sentence as an equation.

\newline

89

is equal to the quotient of

y

17

\newline

/

) if you want to use a division sign.

\newline

Posted 1 month ago

Question

Write the sentence as an equation.

\newline

45

is equal to the quotient of

z

5

\newline

/

) if you want to use a division sign.

\newline

Posted 3 months ago

Question

h

\newline

h^2 + 24h = 0

\newline

Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.

\newline

h =

Posted 3 months ago

Question

h^2 - 4h = 0

Posted 1 month ago

Question

Combine the like terms to create an equivalent expression:

\newline

-k-(-8k)=\square

Posted 4 months ago

Question

Which of the following degree measures is equal to

5 \pi

\newline

(The number of degrees of arc in a circle is

360

. The number of radians of arc in a circle is

2 \pi

\newline

1

\newline

144^{\circ}

\newline

900^{\circ}

\newline

1,080^{\circ}

\newline

1,800^{\circ}

Posted 1 month ago