Algebra Examples

$\cos (θ) \sec (θ) - \frac{\cos (θ)}{\sec (θ)}$

Step 1

Simplify each term.

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Step 1.1

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 1.1.1

Reorder $\cos (θ)$ and $\sec (θ)$ .

$\sec (θ) \cos (θ) - \frac{\cos (θ)}{\sec (θ)}$

Step 1.1.2

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

$\frac{1}{\cos (θ)} \cos (θ) - \frac{\cos (θ)}{\sec (θ)}$

Step 1.1.3

Cancel the common factors.

$1 - \frac{\cos (θ)}{\sec (θ)}$

Step 1.2

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

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

Step 1.3

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\cos (θ)}$ .

$1 - (\cos (θ) \cos (θ))$

Step 1.4

Simplify.

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Step 1.4.1

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

$1 - (\cos^{1} (θ) \cos (θ))$

Step 1.4.2

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

$1 - (\cos^{1} (θ) \cos^{1} (θ))$

Step 1.4.3

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

$1 - {\cos (θ)}^{1 + 1}$

Step 1.4.4

Add $1$ and $1$ .

$1 - \cos^{2} (θ)$

Step 2

Apply pythagorean identity.

$\sin^{2} (θ)$