Trigonometry Examples

$\csc (90 - θ)$

Step 1

Apply the difference of angles identity.

$\frac{\sec (90) \sec (θ) \csc (90) \csc (θ)}{\sec (90) \csc (θ) - \csc (90) \sec (θ)}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Rewrite $\sec (90)$ in terms of sines and cosines.

$\frac{\frac{1}{\cos (90)} \sec (θ) \csc (90) \csc (θ)}{\sec (90) \csc (θ) - \csc (90) \sec (θ)}$

Step 2.2

The exact value of $\cos (90)$ is $0$ .

$\frac{\frac{1}{0} \sec (θ) \csc (90) \csc (θ)}{\sec (90) \csc (θ) - \csc (90) \sec (θ)}$

Step 2.3

The expression contains a division by $0$ . The expression is undefined.

Undefined

$\frac{\frac{1}{0} \sec (θ) \csc (90) \csc (θ)}{\sec (90) \csc (θ) - \csc (90) \sec (θ)}$

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

Rewrite $\sec (90)$ in terms of sines and cosines.

$\frac{\frac{1}{0} \sec (θ) \csc (90) \csc (θ)}{\frac{1}{\cos (90)} \csc (θ) - \csc (90) \sec (θ)}$

Step 3.2

The exact value of $\cos (90)$ is $0$ .

$\frac{\frac{1}{0} \sec (θ) \csc (90) \csc (θ)}{\frac{1}{0} \csc (θ) - \csc (90) \sec (θ)}$

Step 3.3

The expression contains a division by $0$ . The expression is undefined.

Undefined

$\frac{\frac{1}{0} \sec (θ) \csc (90) \csc (θ)}{\frac{1}{0} \csc (θ) - \csc (90) \sec (θ)}$

Step 4

The expression contains a division by $0$ . The expression is undefined.

Undefined