Algebra Examples

$- \sin^{2} (θ) (\csc^{2} (θ) - 1)$

Step 1

Apply pythagorean identity.

$- \sin^{2} (θ) \cot^{2} (θ)$

Step 2

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

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

Step 3

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

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

Step 4

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

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Step 4.1

Factor $\sin^{2} (θ)$ out of $- \sin^{2} (θ)$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

$- 1 \cos^{2} (θ)$

Step 5

Rewrite $- 1 \cos^{2} (θ)$ as $- \cos^{2} (θ)$ .

$- \cos^{2} (θ)$