What is the general solution for cos(2x+pi/3)=sin(3x) ?

The general solution for cos(2x+pi/3)=sin(3x) is x=(12pin+pi)/(30),x=pi-pi/6+2pin

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cos(2x+pi/3)=sin(3x)

cos (2 x + \frac{π}{3}) = sin (3 x)

x = \frac{12 πn + π}{30}, x = π - \frac{π}{6} + 2 πn

Solution steps

cos (2 x + \frac{π}{3}) = sin (3 x)

Rewrite using trig identities

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

Apply trig inverse properties

3 x = \frac{π}{2} - (2 x + \frac{π}{3}) + 2 πn, 3 x = π - (\frac{π}{2} - (2 x + \frac{π}{3})) + 2 πn

3 x = \frac{π}{2} - (2 x + \frac{π}{3}) + 2 πn : x = \frac{12 πn + π}{30}

3 x = π - (\frac{π}{2} - (2 x + \frac{π}{3})) + 2 πn : x = π - \frac{π}{6} + 2 πn

x = \frac{12 πn + π}{30}, x = π - \frac{π}{6} + 2 πn

y, x = arcsin (y)

2 sin^{2} (x) + 5 sin (x) = 3

∣ sin (x) ∣ = \frac{1}{2}

sec^{2} (θ) = 2 tan (θ)

2 sin (2 x) + 2 = 0

What is the general solution for cos(2x+pi/3)=sin(3x) ?
The general solution for cos(2x+pi/3)=sin(3x) is x=(12pin+pi)/(30),x=pi-pi/6+2pin