verify that the equation is an identity. (hint: sin 2x = sin (x + x)) sin 2x = 2 sin x cos x substitute 2x =…

verify that the equation is an identity. (hint: sin 2x = sin (x + x)) sin 2x = 2 sin x cos x substitute 2x = x + x and apply the sine of a sum identity. sin 2x = sin (x + x) =

verify that the equation is an identity. (hint: sin 2x = sin (x + x)) sin 2x = 2 sin x cos x substitute 2x = x + x and apply the sine of a sum identity. sin 2x = sin (x + x) =

Answer

Explanation:

Step1: Recall sine - of - sum formula

The sine of a sum formula is $\sin(A + B)=\sin A\cos B+\cos A\sin B$. Here $A = B=x$, so $\sin(x + x)=\sin x\cos x+\cos x\sin x$.

Step2: Simplify the right - hand side

$\sin x\cos x+\cos x\sin x = 2\sin x\cos x$.

Answer:

$2\sin x\cos x$