Expand Using Sum/Difference Formulas sin(75)

Problem

sin(75)

Solution

1. Identify two common angles from the unit circle that sum to 75

75=45+30

2. Apply the formula for the sine of a sum, which is sin(A+B)=sin(A)*cos(B)+cos(A)*sin(B)

sin(45+30)=sin(45)*cos(30)+cos(45)*sin(30)

3. Substitute the exact values for the sine and cosine of 45 and 30

sin(45+30)=√(,2)/2⋅√(,3)/2+√(,2)/2⋅1/2

4. Simplify the expression by performing the multiplication and addition.

sin(75)=√(,6)/4+√(,2)/4

Final Answer

sin(75)=(√(,6)+√(,2))/4

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