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

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

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

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

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

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

sin (x) = 1 : x = \frac{π}{2} + 2 πn

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

Combine all the solutions

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

7 cos^{2} (θ) + 11 cos (θ) = cos (θ) - 3

cos^{2} (x) - 9 cos (x) - 1 = 0

3 tan (x) = 2 sin (x)

12 arcsin (x) = 4 π

sec (x) = 2, 0 \leq x \leq 2 π

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