# 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 to get .

Using the Binomial Theorem, expand to .

Simplify each term.

Remove parentheses around .

Apply the product rule to .

Rewrite as .

Rewrite as .

Multiply by to get .

Apply the product rule to .

Rewrite as .

Factor out .

Add multiplication sign between and .

Rewrite as .

Multiply by to get .

Rewrite as .

Multiply by to get .

Remove parentheses around .

Apply the product rule to .

Rewrite as .

Rewrite as .

Rewrite as .

Raise to the power of to get .

Multiply by to get .

Apply the product rule to .

Factor out .

Rewrite as .

Rewrite as .

Rewrite as .

Raise to the power of to get .

Multiply by to get .

Remove parentheses around .

Apply the product rule to .

Factor out .

Rewrite as .

Rewrite as .

Rewrite as .

Raise to the power of to get .

Multiply by to get .

Rewrite as .

Rewrite as .

Multiply by to get .

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 to get .

Multiply by to get .

Rewrite as .

Multiply by to get .

Rewrite as .

Reorder factors in .

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