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

The general solution for 3+3cos(x)=2(1-cos^2(x)) is x=pi+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin

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

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

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

Solution steps

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

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

sin (x) = 1.5

cot^{2} (θ) - 4 csc (θ) = - 5

tan (θ) = \frac{2}{7}

- 5 sin (3 x - π) = 0

tan (\frac{1}{2} x) = 0

What is the general solution for 3+3cos(x)=2(1-cos^2(x)) ?
The general solution for 3+3cos(x)=2(1-cos^2(x)) is x=pi+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin