# Trigonometry Examples

Step 1

Step 1.1

Reorder and .

Step 1.2

Rewrite as .

Step 1.3

Factor out of .

Step 1.4

Factor out of .

Step 1.5

Rewrite as .

Step 2

Apply pythagorean identity.

Step 3

Step 3.1

Simplify each term.

Step 3.1.1

Rewrite in terms of sines and cosines.

Step 3.1.2

Apply the product rule to .

Step 3.2

Apply the distributive property.

Step 4

Step 4.1

Combine and .

Step 4.2

Multiply by by adding the exponents.

Step 4.2.1

Use the power rule to combine exponents.

Step 4.2.2

Add and .

Step 5

Step 5.1

Multiply by .

Step 5.2

Multiply by .

Step 6

Step 6.1

Rewrite as .

Step 6.2

Reorder and .

Step 7

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Step 8

Step 8.1

Simplify each term.

Step 8.1.1

Factor out of .

Step 8.1.2

Separate fractions.

Step 8.1.3

Convert from to .

Step 8.1.4

Divide by .

Step 8.2

Simplify each term.

Step 8.2.1

Factor out of .

Step 8.2.2

Separate fractions.

Step 8.2.3

Convert from to .

Step 8.2.4

Divide by .

Step 9

Step 9.1

Apply the distributive property.

Step 9.2

Apply the distributive property.

Step 9.3

Apply the distributive property.

Step 10

Step 10.1

Combine the opposite terms in .

Step 10.1.1

Reorder the factors in the terms and .

Step 10.1.2

Add and .

Step 10.1.3

Add and .

Step 10.2

Simplify each term.

Step 10.2.1

Multiply .

Step 10.2.1.1

Raise to the power of .

Step 10.2.1.2

Raise to the power of .

Step 10.2.1.3

Use the power rule to combine exponents.

Step 10.2.1.4

Add and .

Step 10.2.2

Rewrite using the commutative property of multiplication.

Step 10.2.3

Multiply .

Step 10.2.3.1

Raise to the power of .

Step 10.2.3.2

Raise to the power of .

Step 10.2.3.3

Use the power rule to combine exponents.

Step 10.2.3.4

Add and .

Step 10.2.4

Multiply .

Step 10.2.4.1

Raise to the power of .

Step 10.2.4.2

Raise to the power of .

Step 10.2.4.3

Use the power rule to combine exponents.

Step 10.2.4.4

Add and .