Question

question 4 (1 point)
which expression is equivalent to \frac{\sin 2x}{2\sin^{2}x}
\bigcirc a) 2\csc x
\bigcirc b) \frac{2}{\sin x}
\bigcirc c) \cot x
\bigcirc d) \tan x

Explanation:

Step1: Use double - angle formula

We know that \(\sin2x = 2\sin x\cos x\). So the given expression \(\frac{\sin2x}{2\sin^{2}x}\) becomes \(\frac{2\sin x\cos x}{2\sin^{2}x}\).

Step2: Simplify the expression

Cancel out the common factors \(2\) and \(\sin x\) (assuming \(\sin x
eq0\)) in the numerator and denominator. \(\frac{2\sin x\cos x}{2\sin^{2}x}=\frac{\cos x}{\sin x}\).

Step3: Use trigonometric identity

Since \(\frac{\cos x}{\sin x}=\cot x\).

Answer:

C. \(\cot x\)