Simplify sin((5pi)/12)cos(pi/3)+cos((5pi)/12)sin(pi/3)

Simplify sin((5pi)/12)cos(pi/3)+cos((5pi)/12)sin(pi/3)
Simplify terms.
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Simplify each term.
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The exact value of is .
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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 .
Multiply by .
Multiply .
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Multiply and .
Combine using the product rule for radicals.
Multiply by .
Multiply by .
Combine the numerators over the common denominator.
The exact value of is .
Multiply .
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Multiply and .
Multiply by .
The exact value of is .
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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 exact value of is .
Multiply .
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Multiply and .
Multiply by .
Apply the distributive property.
Combine using the product rule for radicals.
Multiply .
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Combine using the product rule for radicals.
Multiply by .
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.
Combine the numerators over the common denominator.
Simplify the numerator.
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Add and .
Subtract from .
Add 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 .
Cancel the common factor.
Rewrite the expression.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
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