simplify cot(x)*sin(x)

The cotangent is read as

\cot (u) = \frac{\cos (u)}{\sin (u)}

, on each interval where

\sin (u) \neq 0

Let's simplify:

\frac{\cos (x)}{\sin (x)} \cdot \sin (x)

Use the double-angle formula:

2 \cdot \sin (x) \cdot \cos (x) = \sin (2 x)

ⅰ

\cos (x) \cdot \sin (x)

\frac{1}{2} \cdot \sin (2 x)

\frac{\frac{1}{2} \cdot \sin (2 x)}{\sin (x)}

ⓘ Multiplying a fraction by a term multiplies its numerator:

\frac{1}{2} \cdot \sin (2 x)

\frac{1 \cdot \sin (2 x)}{2}

\frac{\sin (2 x)}{2}

\frac{\frac{\sin (2 x)}{2}}{\sin (x)}

ⓘ Dividing a fraction by

\sin (x)

is multiplying its denominator by

\sin (x)

\frac{\frac{\sin (2 x)}{2}}{\sin (x)}

\frac{\sin (2 x)}{2 \cdot \sin (x)}

▶Simplified form:

\frac{\sin (2 x)}{2 \cdot \sin (x)}

100% free