# 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.
Simplify each term.
The exact value of is .
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 .
Simplify each term.
Multiply .
Multiply and .
Multiply by .
Multiply .
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 .
Multiply and .
Multiply by .
The exact value of is .
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 .
Simplify each term.
Multiply .
Multiply and .
Combine using the product rule for radicals.
Multiply by .
Multiply by .
Multiply .
Multiply and .
Multiply by .
Combine the numerators over the common denominator.
The exact value of is .
Multiply .
Multiply and .
Multiply by .
Apply the distributive property.
Combine using the product rule for radicals.
Multiply .
Combine using the product rule for radicals.
Multiply by .
Simplify each term.
Multiply by .
Rewrite as .
Factor out of .
Rewrite as .
Pull terms out from under the radical.
Combine the numerators over the common denominator.
Simplify the numerator.