Simplify (sin(2x))/(2sin(x))

Problem

sin(2*x)/(2*sin(x))

Solution

1. Apply the double angle identity for the sine function, which states that sin(2*x)=2*sin(x)*cos(x)

2. Substitute this identity into the numerator of the expression.

(2*sin(x)*cos(x))/(2*sin(x))

3. Cancel the common factors of 2 and sin(x) from the numerator and the denominator.

cos(x)

Final Answer

sin(2*x)/(2*sin(x))=cos(x)

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