Trigonometry Examples

$\sin^{2} (x) \cos (x) \csc^{3} (x) \sec (x)$

Step 1

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

$\sin^{2} (x) \cos (x) {(\frac{1}{\sin (x)})}^{3} \sec (x)$

Step 2

Simplify the expression.

Tap for more steps...

Step 2.1

Apply the product rule to $\frac{1}{\sin (x)}$ .

$\sin^{2} (x) \cos (x) \frac{1^{3}}{\sin^{3} (x)} \sec (x)$

Step 2.2

One to any power is one.

$\sin^{2} (x) \cos (x) \frac{1}{\sin^{3} (x)} \sec (x)$

Step 3

Cancel the common factor of $\sin^{2} (x)$ .

Tap for more steps...

Step 3.1

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

$\sin^{2} (x) (\cos (x)) \frac{1}{\sin^{3} (x)} \sec (x)$

Step 3.2

Factor $\sin^{2} (x)$ out of $\sin^{3} (x)$ .

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

Step 3.3

Cancel the common factor.

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

Step 3.4

Rewrite the expression.

$\cos (x) \frac{1}{\sin (x)} \sec (x)$

Step 4

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

$\frac{\cos (x)}{\sin (x)} \sec (x)$

Step 5

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

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

Step 6

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

Tap for more steps...

Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

$\frac{1}{\sin (x)}$

Step 7

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\csc (x)$