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

The general solution for 3sin(x)-2cos^2(x)=0 is x= pi/6+2pin,x=(5pi)/6+2pin

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

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

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x) = - 2 :

No Solution

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

4 cos^{2} (x) + 4 cos (x) - 3 = 0

sin (4 x) cos (x) - cos (4 x) sin (x) = 0

2 sin (x) - (2 - 2) = 2 csc (x)

5 sin (62.83 x) = - 0.32

6 cos^{2} (θ) - 5 = 6 sin^{2} (θ) + sin (θ)

What is the general solution for 3sin(x)-2cos^2(x)=0 ?
The general solution for 3sin(x)-2cos^2(x)=0 is x= pi/6+2pin,x=(5pi)/6+2pin