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

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

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

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

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

Solution steps

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

Subtract

2 cos^{2} (x)

from both sides

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

sin^{2} (θ) - cos^{2} (θ) = 0

sec (x) = tan (x) + 1

5 cos (2 x) + 1 = 3 cos (2 x)

2 sin (4 x) + 6 = 5

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