What is the general solution for 2sin^2(x)-3cos(x)=0 ?

The general solution for 2sin^2(x)-3cos(x)=0 is x= pi/3+2pin,x=(5pi)/3+2pin

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2sin^2(x)-3cos(x)=0

2 sin^{2} (x) - 3 cos (x) = 0

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

2 sin^{2} (x) - 3 cos (x) = 0

Rewrite using trig identities

(1 - cos^{2} (x)) \cdot 2 - 3 cos (x) = 0

Solve by substitution

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

cos (x) = - 2 :

No Solution

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sin (θ) = \frac{2}{9}

- 2 sin^{2} (θ) + 9 sin (θ) = 8 sin (θ) - 1

sin^{2} (x) - sin (x) - 1 = 0

2 sec (x) - 4 = 0

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

What is the general solution for 2sin^2(x)-3cos(x)=0 ?
The general solution for 2sin^2(x)-3cos(x)=0 is x= pi/3+2pin,x=(5pi)/3+2pin