Trigonometry Examples

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

Step 1

Simplify with factoring out.

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Step 1.1

Reorder $\cos^{2} (t)$ and $- 1$ .

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

Step 1.2

Rewrite $- 1$ as $- 1 (1)$ .

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

Step 1.3

Factor $- 1$ out of $\cos^{2} (t)$ .

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

Step 1.4

Factor $- 1$ out of $- 1 (1) - 1 (- \cos^{2} (t))$ .

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

Step 1.5

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

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

Step 2

Apply pythagorean identity.

$\frac{- \sin^{2} (t)}{\sin (t)}$

Step 3

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

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Step 3.1

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

$\frac{\sin (t) (- \sin (t))}{\sin (t)}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\frac{\sin (t) (- \sin (t))}{\sin (t) \cdot 1}$

Step 3.2.2

Cancel the common factor.

$\frac{\sin (t) (- \sin (t))}{\sin (t) \cdot 1}$

Step 3.2.3

Rewrite the expression.

$\frac{- \sin (t)}{1}$

Step 3.2.4

Divide $- \sin (t)$ by $1$ .

$- \sin (t)$