Simplify (sin(theta)sec(theta))/(cot(theta))

$\frac{\sin (θ) \sec (θ)}{\cot (θ)}$

Step 1

Separate fractions.

$\frac{\sec (θ)}{1} \cdot \frac{\sin (θ)}{\cot (θ)}$

Step 2

Rewrite $\cot (θ)$ in terms of sines and cosines.

$\frac{\sec (θ)}{1} \cdot \frac{\sin (θ)}{\frac{\cos (θ)}{\sin (θ)}}$

Step 3

Multiply by the reciprocal of the fraction to divide by $\frac{\cos (θ)}{\sin (θ)}$ .

$\frac{\sec (θ)}{1} (\sin (θ) \frac{\sin (θ)}{\cos (θ)})$

Step 4

Write $\sin (θ)$ as a fraction with denominator $1$ .

$\frac{\sec (θ)}{1} (\frac{\sin (θ)}{1} \cdot \frac{\sin (θ)}{\cos (θ)})$

Step 5

Simplify.

Divide $\sin (θ)$ by $1$ .

$\frac{\sec (θ)}{1} (\sin (θ) \frac{\sin (θ)}{\cos (θ)})$

Combine $\sin (θ)$ and $\frac{\sin (θ)}{\cos (θ)}$ .

$\frac{\sec (θ)}{1} \cdot \frac{\sin (θ) \sin (θ)}{\cos (θ)}$

Step 6

Divide $\sec (θ)$ by $1$ .

$\sec (θ) \frac{\sin (θ) \sin (θ)}{\cos (θ)}$

Step 7

Rewrite $\sec (θ)$ in terms of sines and cosines.

$\frac{1}{\cos (θ)} \cdot \frac{\sin (θ) \sin (θ)}{\cos (θ)}$

Step 8

Simplify the numerator.

Raise $\sin (θ)$ to the power of $1$ .

$\frac{1}{\cos (θ)} \cdot \frac{\sin^{1} (θ) \sin (θ)}{\cos (θ)}$

Raise $\sin (θ)$ to the power of $1$ .

$\frac{1}{\cos (θ)} \cdot \frac{\sin^{1} (θ) \sin^{1} (θ)}{\cos (θ)}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{\cos (θ)} \cdot \frac{{\sin (θ)}^{1 + 1}}{\cos (θ)}$

Add $1$ and $1$ .

$\frac{1}{\cos (θ)} \cdot \frac{\sin^{2} (θ)}{\cos (θ)}$

Step 9

Combine fractions.

Combine.

$\frac{1 \sin^{2} (θ)}{\cos (θ) \cos (θ)}$

Multiply $\sin^{2} (θ)$ by $1$ .

$\frac{\sin^{2} (θ)}{\cos (θ) \cos (θ)}$

Step 10

Simplify the denominator.

Raise $\cos (θ)$ to the power of $1$ .

$\frac{\sin^{2} (θ)}{\cos^{1} (θ) \cos (θ)}$

Raise $\cos (θ)$ to the power of $1$ .

$\frac{\sin^{2} (θ)}{\cos^{1} (θ) \cos^{1} (θ)}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sin^{2} (θ)}{{\cos (θ)}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sin^{2} (θ)}{\cos^{2} (θ)}$

Step 11

Convert from $\frac{\sin^{2} (θ)}{\cos^{2} (θ)}$ to $\tan^{2} (θ)$ .

$\tan^{2} (θ)$

Simplify (sin(theta)sec(theta))/(cot(theta))

Related Questions

Support LCMGCF.com by disabling your adblocker.