Find the Exact Value cos(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 .
Simplify .
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Simplify each term.
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Multiply .
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Multiply and .
Combine using the product rule for radicals.
Multiply by .
Multiply by .
Multiply .
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Multiply and .
Multiply by .
Combine the numerators over the common denominator.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Find the Exact Value cos(75)

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