What is sin(3x)cos(x)-cos(3x)sin(x) ?

The solution to sin(3x)cos(x)-cos(3x)sin(x) is sin(3x-x)

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simplify sin(3x)cos(x)-cos(3x)sin(x)

simplify

sin (3 x) cos (x) - cos (3 x) sin (x)

sin (3 x - x)

Solution steps

sin (3 x) cos (x) - cos (3 x) sin (x)

Use the Angle Difference identity:

sin (s) cos (t) - cos (s) sin (t) = sin (s - t)

= sin (3 x - x)

\frac{4}{5} \cdot \frac{5}{6}

\frac{16}{x ^{2} - 16} + \frac{2}{x + 4}

- 2 x^{- 2} y^{4} \cdot (- x^{5} y^{- 3})^{- 5}

\frac{t - 3}{t ^{2} + 9} \cdot \frac{t + 3}{t ^{2} - 9}

\frac{a ^{3} b ^{5}}{a ^{4} b}

What is sin(3x)cos(x)-cos(3x)sin(x) ?
The solution to sin(3x)cos(x)-cos(3x)sin(x) is sin(3x-x)