Split into two angles where the values of the six trigonometric functions are known.

Apply the difference of angles identity.

The exact value of is .

The exact value of is .

The exact value of is .

The exact value of is .

Multiply by .

Multiply by .

Multiply by .

Multiply and .

Expand the denominator using the FOIL method.

Simplify.

Simplify the numerator.

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Simplify .

Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Combine using the product rule for radicals.

Multiply by .

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

Multiply by .

Multiply by .

Multiply by .

Add and .

Add and .

Cancel the common factor of and .

Factor out of .

Factor out of .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Find the Exact Value cot(pi/12)