Simplify

Problem

sin(π/12)*cos((2*π)/3)+cos(π/12)*sin((2*π)/3)

Solution

1. Identify the trigonometric identity that matches the form of the expression. The expression follows the sine addition formula:

sin(A+B)=sin(A)*cos(B)+cos(A)*sin(B)

2. Assign the values for the variables A and B based on the given expression:

A=π/12

B=(2*π)/3

3. Apply the formula by substituting A and B into the sine addition identity:

sin(π/12+(2*π)/3)

4. Find a common denominator to add the fractions inside the sine function:

(2*π)/3=(8*π)/12

5. Add the fractions:

π/12+(8*π)/12=(9*π)/12

6. Simplify the fraction:

(9*π)/12=(3*π)/4

7. Evaluate the sine of the resulting angle using the unit circle:

sin((3*π)/4)=√(,2)/2

Final Answer

sin(π/12)*cos((2*π)/3)+cos(π/12)*sin((2*π)/3)=√(,2)/2

Want more problems? Check here!