sin(A+B)
sinAcosB+cosAsinB
Using the trigonometric identity for the sine of the sum of two angles, we have:
sin(A+B) = sin(A)cos(B) + cos(A)sin(B)
This formula holds true for any two angles A and B. It expresses the sine of their sum in terms of the sines and cosines of the individual angles. It is often used to simplify trigonometric expressions or to solve problems in geometry or physics that involve the addition or subtraction of angles.
To better understand this formula, it may be helpful to consider a geometric interpretation. If A and B are angles in a right triangle, for example, then sin(A) and sin(B) represent the ratios of the opposite sides to the hypotenuse, while cos(A) and cos(B) represent the ratios of the adjacent sides to the hypotenuse. The formula for sin(A+B) then tells us how to combine these ratios to find the sine of the angle that is the sum of A and B.
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