Simplify (cos(2a))/(cos(a)^2)

$\frac{\cos (2 a)}{\cos^{2} (a)}$

Factor $\cos (a)$ out of $\cos^{2} (a)$ .

$\frac{\cos (2 a)}{\cos (a) \cos (a)}$

Separate fractions.

$\frac{1}{\cos (a)} \cdot \frac{\cos (2 a)}{\cos (a)}$

Rewrite $\frac{\cos (2 a)}{\cos (a)}$ as a product.

$\frac{1}{\cos (a)} (\cos (2 a) \frac{1}{\cos (a)})$

Write $\cos (2 a)$ as a fraction with denominator $1$ .

$\frac{1}{\cos (a)} (\frac{\cos (2 a)}{1} \cdot \frac{1}{\cos (a)})$

Simplify.

Divide $\cos (2 a)$ by $1$ .

$\frac{1}{\cos (a)} (\cos (2 a) \frac{1}{\cos (a)})$

Convert from $\frac{1}{\cos (a)}$ to $\sec (a)$ .

$\frac{1}{\cos (a)} (\cos (2 a) \sec (a))$

Convert from $\frac{1}{\cos (a)}$ to $\sec (a)$ .

$\sec (a) (\cos (2 a) \sec (a))$

Multiply $\sec (a) (\cos (2 a) \sec (a))$ .

Raise $\sec (a)$ to the power of $1$ .

$\sec^{1} (a) \sec (a) \cos (2 a)$

Raise $\sec (a)$ to the power of $1$ .

$\sec^{1} (a) \sec^{1} (a) \cos (2 a)$

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

${\sec (a)}^{1 + 1} \cos (2 a)$

Add $1$ and $1$ .

$\sec^{2} (a) \cos (2 a)$