Question

verify that the equation is an identity.
\frac{\cos 2 x}{\sin x}=\cos x \cot x-\sin x
to verify the identity, start with either side and transform it to look like the other side. in this example, we will start with the right side. choose the correct transformations and transform the expression in
each step.
\cos x \cot x-\sin x=\square
(do not simplify.)

Explanation:

Step1: Substitute cotangent identity

Recall that \(\cot x=\frac{\cos x}{\sin x}\). So, \(\cos x\cot x-\sin x=\cos x\times\frac{\cos x}{\sin x}-\sin x\).

Step2: Simplify the expression

$$
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$$

Step3: Use double - angle formula

Recall the double - angle formula \(\cos2x=\cos^{2}x-\sin^{2}x\). So, \(\frac{\cos^{2}x - \sin^{2}x}{\sin x}=\frac{\cos2x}{\sin x}\)

Answer:

\(\frac{\cos2x}{\sin x}\)