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

Apply the sum of angles identity.

The exact value of is .

The exact value of is .

The exact value of is .

The exact value of is .

The exact value of is .

The exact value of is .

The exact value of is .

The exact value of is .

Simplify the numerator.

Multiply and .

Combine and .

Combine and .

Simplify the denominator.

Multiply by .

Combine and simplify the denominator.

Multiply and .

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 .

Combine and simplify the denominator.

Multiply and .

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.

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Multiply by .

Combine and .

Combine using the product rule for radicals.

Multiply by .

Move the negative in front of the fraction.

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Multiply by .

Simplify the numerator.

Multiply by .

Multiply by .

Simplify the denominator.

Combine using the product rule for radicals.

Multiply by .

Simplify the numerator.

Combine and into a single radical.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Rewrite as .

Any root of is .

Multiply by .

Combine and simplify the denominator.

Multiply and .

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.

Combine and .

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Combine and .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

Multiply and .

Expand the denominator using the FOIL method.

Simplify.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Apply the distributive property.

Multiply .

Combine using the product rule for radicals.

Multiply by .

Combine using the product rule for radicals.

Simplify each term.

Multiply by .

Rewrite as .

Factor out of .

Rewrite as .

Pull terms out from under the radical.

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 sec(75)