Find the Exact Value sec(75)

Math
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 .
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Simplify the numerator.
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Multiply and .
Combine and .
Combine and .
Simplify the denominator.
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Multiply by .
Combine and simplify the denominator.
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Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
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Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Evaluate the exponent.
Multiply by .
Combine and simplify the denominator.
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Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
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Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Evaluate the exponent.
Cancel the common factor of .
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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 .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Multiply by .
Simplify the numerator.
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Multiply by .
Multiply by .
Simplify the denominator.
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Combine using the product rule for radicals.
Multiply by .
Simplify the numerator.
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Combine and into a single radical.
Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Rewrite as .
Any root of is .
Multiply by .
Combine and simplify the denominator.
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Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
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Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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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 .
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Cancel the common factor.
Rewrite the expression.
Combine and .
Combine and .
Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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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 .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Apply the distributive property.
Multiply .
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Combine using the product rule for radicals.
Multiply by .
Combine using the product rule for radicals.
Simplify each term.
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Multiply by .
Rewrite as .
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Factor out of .
Rewrite as .
Pull terms out from under the radical.
Cancel the common factor of and .
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Factor out of .
Factor out of .
Factor out of .
Cancel the common factors.
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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)

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