What is 2sin((pi/3)-2x)+3 ?

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

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simplify 2sin((pi/3)-2x)+3

simplify

2 sin ((\frac{π}{3}) - 2 x) + 3

3 cos (2 x) - sin (2 x) + 3

Solution steps

2 sin ((\frac{π}{3}) - 2 x) + 3

Rewrite using trig identities

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

Expand

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

= 3 cos (2 x) - sin (2 x) + 3

cos (- 9 0^{\circ} + x)

sin (y - π)

cos (arctan (x) + arctan (x))

3 sin (x - 3 0^{\circ})

tan (2 x - \frac{π}{2})

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