Trigonometry Examples

$\cos (x) (\cos (x) - \sec (x))$

Step 1

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

$\cos (x) (\cos (x) - \frac{1}{\cos (x)})$

Step 2

Apply the distributive property.

$\cos (x) \cos (x) + \cos (x) (- \frac{1}{\cos (x)})$

Step 3

Multiply $\cos (x) \cos (x)$ .

Tap for more steps...

Step 3.1

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

$\cos^{1} (x) \cos (x) + \cos (x) (- \frac{1}{\cos (x)})$

Step 3.2

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

$\cos^{1} (x) \cos^{1} (x) + \cos (x) (- \frac{1}{\cos (x)})$

Step 3.3

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

${\cos (x)}^{1 + 1} + \cos (x) (- \frac{1}{\cos (x)})$

Step 3.4

Add $1$ and $1$ .

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

Step 4

Simplify terms.

Tap for more steps...

Step 4.1

Rewrite using the commutative property of multiplication.

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

Step 4.2

Cancel the common factor of $\cos (x)$ .

Tap for more steps...

Step 4.2.1

Factor $\cos (x)$ out of $- \cos (x)$ .

$\cos^{2} (x) + \cos (x) \cdot - 1 \frac{1}{\cos (x)}$

Step 4.2.2

Cancel the common factor.

$\cos^{2} (x) + \cos (x) \cdot - 1 \frac{1}{\cos (x)}$

Step 4.2.3

Rewrite the expression.

$\cos^{2} (x) - 1$

Step 4.3

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

$- 1 + \cos^{2} (x)$

Step 4.4

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

$- 1 (1) + \cos^{2} (x)$

Step 4.5

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

$- 1 (1) - 1 (- \cos^{2} (x))$

Step 4.6

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

$- 1 (1 - \cos^{2} (x))$

Step 4.7

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

$- (1 - \cos^{2} (x))$

Step 5

Apply pythagorean identity.

$- \sin^{2} (x)$