Learn how to solve problems step by step online. Prove the trigonometric identity sin(x)-tan(y)cos(x)=sin(x-y)/cos(y). Starting from the right-hand side (RHS) of the identity. Using the sine of a sum formula: \sin(\alpha\pm\beta)=\sin(\alpha)\cos(\beta)\pm\cos(\alpha)\sin(\beta), where angle \alpha equals x, and angle \beta equals -y. Expand the fraction \frac{\sin\left(x\right)\cos\left(y\right)-\cos\left(x\right)\sin\left(y\right)}{\cos\left(y\right)} into 2 simpler fractions with common denominator \cos\left(y\right). Simplify the resulting fractions.

Prove the trigonometric identity sin(x)-tan(y)cos(x)=sin(x-y)/cos(y)