Apply the sine double–angle identity.

Use the double–angle identity to transform to .

Move .

Apply pythagorean identity.

Add and .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Apply the sine double–angle identity.

Use the double–angle identity to transform to .

Apply the distributive property.

Multiply .

Multiply by .

Multiply by .

Move .

Apply pythagorean identity.

Add and .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Separate fractions.

Convert from to .

Combine and .

Reorder factors in .

Expand (1+sin(2x)+cos(2x))/(1+sin(2x)-cos(2x))