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+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin

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

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

x = π + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 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) = - 1, cos (x) = - \frac{1}{2}

cos (x) = - 1 : x = π + 2 πn

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Combine all the solutions

x = π + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

4 cos (x) = 3 + 8 cos (x)

sin^{2} (θ) - 3 sin (θ) = 0

cos^{2} (x) = \frac{1}{5}

- 3 cos (2 θ) + 5 = 7 sin (θ) + 5

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

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+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin