Trigonometry Examples

$\frac{\sin (θ) \sec (θ)}{\cos (θ) \tan (θ)}$

Step 1

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

$\frac{\sin (θ) \frac{1}{\cos (θ)}}{\cos (θ) \tan (θ)}$

Step 2

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

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

Step 3

Combine $\sin (θ)$ and $\frac{1}{\cos (θ)}$ .

$\frac{\frac{\sin (θ)}{\cos (θ)}}{\cos (θ) \frac{\sin (θ)}{\cos (θ)}}$

Step 4

Combine $\cos (θ)$ and $\frac{\sin (θ)}{\cos (θ)}$ .

$\frac{\frac{\sin (θ)}{\cos (θ)}}{\frac{\cos (θ) \sin (θ)}{\cos (θ)}}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Reduce the expression $\frac{\cos (θ) \sin (θ)}{\cos (θ)}$ by cancelling the common factors.

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Step 5.1.1

Cancel the common factor.

$\frac{\frac{\sin (θ)}{\cos (θ)}}{\frac{\cos (θ) \sin (θ)}{\cos (θ)}}$

Step 5.1.2

Rewrite the expression.

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

Step 5.2

Divide $\sin (θ)$ by $1$ .

$\frac{\frac{\sin (θ)}{\cos (θ)}}{\sin (θ)}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{\sin (θ)}{\cos (θ)} \cdot \frac{1}{\sin (θ)}$

Step 7

Cancel the common factor of $\sin (θ)$ .

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Step 7.1

Cancel the common factor.

$\frac{\sin (θ)}{\cos (θ)} \cdot \frac{1}{\sin (θ)}$

Step 7.2

Rewrite the expression.

$\frac{1}{\cos (θ)}$

Step 8

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

$\sec (θ)$