What is the general solution for -2cos^2(x)=3(sin(x)-1) ?

The general solution for -2cos^2(x)=3(sin(x)-1) is x= pi/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin

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-2cos^2(x)=3(sin(x)-1)

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

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

Solution steps

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

Subtract

3 (sin (x) - 1)

from both sides

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

cos (x) tan (x) = sin (2 x)

2 ∣ sin (4 θ) ∣ = 0

250 sin (7 5^{\circ}) = 393.19 sin (4 5^{\circ} - θ)

tan (θ) = \frac{6}{6.71}

x, sin (x) - 1 = 0

What is the general solution for -2cos^2(x)=3(sin(x)-1) ?
The general solution for -2cos^2(x)=3(sin(x)-1) is x= pi/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin