Simplify sin(25)cos(35)+cos(25)sin(35)

Problem

sin(25)*cos(35)+cos(25)*sin(35)

Solution

1. Identify the trigonometric identity that matches the structure of the expression. The expression follows the form sin(A)*cos(B)+cos(A)*sin(B)

2. Recall the sine addition formula, which states that sin(A+B)=sin(A)*cos(B)+cos(A)*sin(B)

3. Substitute the given values A=25 and B=35 into the identity.

sin(25+35)

4. Add the angles inside the sine function.

25+35=60

5. Evaluate the resulting trigonometric value using the unit circle or special triangles.

sin(60)=√(,3)/2

Final Answer

sin(25)*cos(35)+cos(25)*sin(35)=√(,3)/2

Want more problems? Check here!