# Trigonometry Examples

A good method to expand is by using DeMoivre's theorem . When , .

Expand the right hand side of using the binomial theorem.

Expand:

Multiply by .

Using the Binomial Theorem, expand to .

Simplify each term.

Remove parentheses around .

Apply the product rule to .

Rewrite as .

Rewrite as .

Multiply by .

Apply the product rule to .

Rewrite as .

Factor out .

Add multiplication sign between and .

Rewrite as .

Multiply by .

Rewrite as .

Multiply by .

Remove parentheses around .

Apply the product rule to .

Rewrite as .

Rewrite as .

Rewrite as .

Raise to the power of .

Multiply by .

Apply the product rule to .

Factor out .

Rewrite as .

Rewrite as .

Rewrite as .

Raise to the power of .

Multiply by .

Remove parentheses around .

Apply the product rule to .

Factor out .

Rewrite as .

Rewrite as .

Rewrite as .

Raise to the power of .

Multiply by .

Rewrite as .

Rewrite as .

Multiply by .

Apply the product rule to .

Rewrite as .

Factor out .

Factor out .

Add multiplication sign between and .

Rewrite as .

Rewrite as .

Rewrite as .

Raise to the power of .

Multiply by .

Rewrite as .

Multiply by .

Rewrite as .

Multiply by .

Remove parentheses around .

Apply the product rule to .

Rewrite as .

Rewrite as .

Rewrite as .

Rewrite as .

Raise to the power of .

Remove parentheses around .

One to any power is one.

Multiply by .

Reorder factors in .

Take out the expressions with the imaginary part, which are equal to . Remove the imaginary number .