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 cos (x) + 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

3 tan (x) + 2 = - 3

sec (2 θ) = csc (7 0^{\circ})

- 4 cos^{2} (θ) + 1 = 0

sin (2 x) - sin (4 x) + sin (6 x) = 0

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