prove the identity. sinx cos(x - y) - cosx sin(x - y) = siny note that each statement must be based on a…

prove the identity. sinx cos(x - y) - cosx sin(x - y) = siny note that each statement must be based on a rule chosen from the rule menu. to see a detailed description of the right of the rule. statement rule sinx cos(x - y) - cosx sin(x - y) select rule

prove the identity. sinx cos(x - y) - cosx sin(x - y) = siny note that each statement must be based on a rule chosen from the rule menu. to see a detailed description of the right of the rule. statement rule sinx cos(x - y) - cosx sin(x - y) select rule

Answer

Explanation:

Step1: Apply the sine - difference formula

Recall the formula $\sin(A - B)=\sin A\cos B-\cos A\sin B$. Here, if we let $A = x$ and $B=(x - y)$, then $\sin x\cos(x - y)-\cos x\sin(x - y)=\sin(x-(x - y))$. $\sin x\cos(x - y)-\cos x\sin(x - y)=\sin(x-(x - y))$

Step2: Simplify the argument of the sine function

Simplify the expression inside the sine function: $x-(x - y)=x - x + y=y$. So, $\sin(x-(x - y))=\sin y$. $\sin(x-(x - y))=\sin y$

Answer:

The identity $\sin x\cos(x - y)-\cos x\sin(x - y)=\sin y$ is proved.