What is sin(x)-sin(x-120) ?

The solution to sin(x)-sin(x-120) is 3/2 sin(x)+(sqrt(3))/2 cos(x)

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simplify sin(x)-sin(x-120)

simplify

sin (x) - sin (x - 12 0^{\circ})

\frac{3}{2} sin (x) + \frac{3}{2} cos (x)

Solution steps

sin (x) - sin (x - 12 0^{\circ})

Rewrite using trig identities

= sin (x) - (- \frac{1}{2} sin (x) - \frac{3}{2} cos (x))

Simplify

sin (x) - (- \frac{1}{2} sin (x) - \frac{3}{2} cos (x)) : \frac{3}{2} sin (x) + \frac{3}{2} cos (x)

= \frac{3}{2} sin (x) + \frac{3}{2} cos (x)

sin (\frac{5 π}{2} + 2 a)

cos (θ - 9 0^{\circ})

- 2 sin (2 x + π) + 1

sin (π + θ) + cos (\frac{π}{2} - θ)

2 sin (2 x - \frac{π}{3}) + 1

What is sin(x)-sin(x-120) ?
The solution to sin(x)-sin(x-120) is 3/2 sin(x)+(sqrt(3))/2 cos(x)