Expand Using Sum/Difference Formulas cos(345)

Expand Using Sum/Difference Formulas cos(345)
First, split the angle into two angles where the values of the six trigonometric functions are known. In this case, can be split into .
Use the sum formula for cosine to simplify the expression. The formula states that .
The exact value of is .
Simplify .
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Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
The exact value of is .
The exact value of is .
Simplify .
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Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth quadrant.
The exact value of is .
Simplify each term.
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Multiply .
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Multiply and .
Multiply by .
Multiply .
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Multiply by .
Multiply by .
Multiply and .
Combine using the product rule for radicals.
Multiply by .
Multiply by .
Combine the numerators over the common denominator.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
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