First, split the angle into two angles where the values of the six trigonometric functions are known. In this case, can be split into .

Use the difference formula for tangent to simplify the expression. The formula states that .

The exact value of is .

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

The exact value of is .

The exact value of is .

Multiply by .

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

The exact value of is .

Multiply by .

Multiply and .

Expand the denominator using the FOIL method.

Simplify.

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify each term.

Multiply by .

Multiply by .

Multiply by .

Multiply .

Multiply by .

Multiply by .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Rewrite as .

Apply the power rule and multiply exponents, .

Combine and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Evaluate the exponent.

Add and .

Subtract from .

Factor out of .

Factor out of .

Factor out of .

Move the negative one from the denominator of .

Rewrite as .

Apply the distributive property.

Multiply by .

Multiply by .

Multiply by .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Expand Using Sum/Difference Formulas tan(-195)