Mastering Trigonometric Identity: How to Calculate Sin(A-B) Using Angle Subtraction Formula

sin(A-B)

sinAcosB-cosAsinB

To find sin(A-B), we can use the trigonometric identity:

sin(A-B) = sin A cos B – cos A sin B

where A and B are the angles in radians.

This formula is derived from the angle subtraction formula for sine:

sin(A-B) = sin A cos (-B) – cos A sin (-B)

Note that cos(-B) = cos B and sin(-B) = -sin B.

Substituting these values in the formula, we get:

sin(A-B) = sin A cos B – cos A sin B

Therefore, sin(A-B) can be calculated by taking the sine of angle A, multiplying it by the cosine of angle B and subtracting the cosine of angle A multiplied by the sine of angle B.

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