# Find the Exact Value sec(75) 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 .
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.
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.
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.
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:
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