Algebra Examples

$\sin^{2} (θ) \cot^{2} (θ) \tan^{2} (θ) \csc^{2} (θ)$

Step 1

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

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

Step 2

Apply the product rule to $\frac{\cos (θ)}{\sin (θ)}$ .

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

Step 3

Cancel the common factor of $\sin^{2} (θ)$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$\cos^{2} (θ) \tan^{2} (θ) \csc^{2} (θ)$

Step 4

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

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

Step 5

Apply the product rule to $\frac{\sin (θ)}{\cos (θ)}$ .

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

Step 6

Cancel the common factor of $\cos^{2} (θ)$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$\sin^{2} (θ) \csc^{2} (θ)$

Step 7

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

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

Step 8

Simplify the expression.

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Step 8.1

Apply the product rule to $\frac{1}{\sin (θ)}$ .

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

Step 8.2

One to any power is one.

$\sin^{2} (θ) \frac{1}{\sin^{2} (θ)}$

Step 9

Cancel the common factor of $\sin^{2} (θ)$ .

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Step 9.1

Cancel the common factor.

$\sin^{2} (θ) \frac{1}{\sin^{2} (θ)}$

Step 9.2

Rewrite the expression.

$1$