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 .

Simplify .

Simplify each term.

Multiply .

Multiply and .

Combine using the product rule for radicals.

Multiply by .

Multiply by .

Multiply .

Multiply and .

Multiply by .

Combine the numerators over the common denominator.

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 .

Simplify .

Simplify each term.

Multiply .

Multiply and .

Combine using the product rule for radicals.

Multiply by .

Multiply by .

Multiply .

Multiply and .

Multiply by .

Combine the numerators over the common denominator.

Multiply and .

Multiply by .

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

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.

Combine using the product rule for radicals.

Multiply by .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

Multiply .

Combine using the product rule for radicals.

Multiply by .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

Multiply by .

Multiply .

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.

Multiply by .

Subtract from .

Subtract from .

Add and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Find the Exact Value sin(pi/12)cos(pi/12)