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

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

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

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

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

Solution steps

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

Subtract

3

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

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

cos (x) = 1 : x = 2 πn

Combine all the solutions

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

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

2 sin (2 x) = 1, 0 \leq x \leq 2 π

sin (θ) = \frac{1}{4}

2 sin (θ) + 3 = 2

3 sin (θ) + cos (θ) = 0

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