Trigonometry Examples

$\frac{1 - \sin^{2} (x)}{\csc^{2} (x - 1)}$

Step 1

Apply pythagorean identity.

$\frac{\cos^{2} (x)}{\csc^{2} (x - 1)}$

Step 2

Rewrite $\frac{\cos^{2} (x)}{\csc^{2} (x - 1)}$ as ${(\frac{\cos (x)}{\csc (x - 1)})}^{2}$ .

${(\frac{\cos (x)}{\csc (x - 1)})}^{2}$

Step 3

Rewrite $\csc (x - 1)$ in terms of sines and cosines.

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

Step 4

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\sin (x - 1)}$ .

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

Step 5

Apply the product rule to $\cos (x) \sin (x - 1)$ .

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