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

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

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

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

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) + 1)

Subtract

3 (cos (x) + 1)

from both sides

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

tan^{2} (θ) - 6 tan (θ) + 5 = 0

tan (4 θ) = - 1

cot (x) (tan (x) - 1) = 0

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

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