Trigonometry Examples

$\frac{\sec^{2} (θ) - \tan^{2} (θ)}{\cot^{2} (θ) - \csc^{2} (θ)}$

Step 1

Apply pythagorean identity.

$\frac{1}{\cot^{2} (θ) - \csc^{2} (θ)}$

Step 2

Simplify with factoring out.

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Step 2.1

Reorder $\cot^{2} (θ)$ and $- \csc^{2} (θ)$ .

$\frac{1}{- \csc^{2} (θ) + \cot^{2} (θ)}$

Step 2.2

Factor $- 1$ out of $- \csc^{2} (θ)$ .

$\frac{1}{- (\csc^{2} (θ)) + \cot^{2} (θ)}$

Step 2.3

Factor $- 1$ out of $\cot^{2} (θ)$ .

$\frac{1}{- (\csc^{2} (θ)) - 1 (- \cot^{2} (θ))}$

Step 2.4

Factor $- 1$ out of $- (\csc^{2} (θ)) - 1 (- \cot^{2} (θ))$ .

$\frac{1}{- (\csc^{2} (θ) - \cot^{2} (θ))}$

Step 3

Apply pythagorean identity.

$\frac{1}{- 1 \cdot 1}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $1$ .

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Step 4.1.1

Cancel the common factor.

$\frac{1}{- 1 \cdot 1}$

Step 4.1.2

Rewrite the expression.

$\frac{1}{- 1}$

Step 4.1.3

Move the negative one from the denominator of $\frac{1}{- 1}$ .

$- 1 \cdot 1$

Step 4.2

Multiply $- 1$ by $1$ .

$- 1$