sin(A-B)
sinAcosB-cosAsinB
The formula for the sine of difference of two angles is:
sin(A – B) = sin(A)cos(B) – cos(A)sin(B)
This formula is known as the sine of difference formula or the angle subtraction formula in trigonometry.
The formula states that the sine of the difference of two angles A and B is equal to the sine of A times the cosine of B minus the cosine of A times the sine of B.
To apply the formula, simply substitute the values of A and B into the equation and compute the results using the values of sine, cosine and tangent of A and B. Remember to use the values of sine, cosine and tangent corresponding to the given angles in either degrees or radians.
For example, let’s say we are given the expression sin(60° – 30°). Using the sine of difference formula, we have:
sin(60° – 30°) = sin(60°)cos(30°) – cos(60°)sin(30°)
Since the values of sine, cosine and tangent for 30° and 60° are known, we can plug them in to get:
sin(60° – 30°) = (sqrt(3)/2)(sqrt(3)/2) – (1/2)(1/2)
Calculate the results and we get:
sin(60° – 30°) = (3/4) – (1/4) = 1/2
Therefore, sin(60° – 30°) = 1/2.
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