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

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

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

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

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

Solution steps

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

Subtract

3

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

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

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

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

x, y = cos (x)

sin (6 x) = 0

sin (x) = 3

1 + sin (x) = 0

sin^{2} (x) - \frac{1}{4} = 0

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