Trigonometry Examples

$\frac{\cos^{2} (x) + 16 \cos (x) + 64}{\cos (x) + 8}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Let $u = \cos (x)$ . Substitute $u$ for all occurrences of $\cos (x)$ .

$\frac{u^{2} + 16 u + 64}{\cos (x) + 8}$

Step 1.2

Factor using the perfect square rule.

Tap for more steps...

Step 1.2.1

Rewrite $64$ as $8^{2}$ .

$\frac{u^{2} + 16 u + 8^{2}}{\cos (x) + 8}$

Step 1.2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$16 u = 2 \cdot u \cdot 8$

Step 1.2.3

Rewrite the polynomial.

$\frac{u^{2} + 2 \cdot u \cdot 8 + 8^{2}}{\cos (x) + 8}$

Step 1.2.4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = u$ and $b = 8$ .

$\frac{{(u + 8)}^{2}}{\cos (x) + 8}$

Step 1.3

Replace all occurrences of $u$ with $\cos (x)$ .

$\frac{{(\cos (x) + 8)}^{2}}{\cos (x) + 8}$

Step 2

Cancel the common factor of ${(\cos (x) + 8)}^{2}$ and $\cos (x) + 8$ .

Tap for more steps...

Step 2.1

Factor $\cos (x) + 8$ out of ${(\cos (x) + 8)}^{2}$ .

$\frac{(\cos (x) + 8) (\cos (x) + 8)}{\cos (x) + 8}$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Multiply by $1$ .

$\frac{(\cos (x) + 8) (\cos (x) + 8)}{(\cos (x) + 8) \cdot 1}$

Step 2.2.2

Cancel the common factor.

$\frac{(\cos (x) + 8) (\cos (x) + 8)}{(\cos (x) + 8) \cdot 1}$

Step 2.2.3

Rewrite the expression.

$\frac{\cos (x) + 8}{1}$

Step 2.2.4

Divide $\cos (x) + 8$ by $1$ .

$\cos (x) + 8$