# Trigonometry Examples

Step 1

Start on the left side.

Step 2

Step 2.1

Write in sines and cosines using the quotient identity.

Step 2.2

Write in sines and cosines using the quotient identity.

Step 3

Step 3.1

To write as a fraction with a common denominator, multiply by .

Step 3.2

To write as a fraction with a common denominator, multiply by .

Step 3.3

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Step 3.3.1

Multiply by .

Step 3.3.2

Multiply by .

Step 3.3.3

Reorder the factors of .

Step 3.4

Combine the numerators over the common denominator.

Step 4

Simplify each term.

Step 5

Step 5.1

Rearrange terms.

Step 5.2

Apply pythagorean identity.

Step 6

Rewrite as .

Step 7

Because the two sides have been shown to be equivalent, the equation is an identity.

is an identity