What is the general solution for 4sin^2(x)=5-4cos(x) ?

The general solution for 4sin^2(x)=5-4cos(x) is x= pi/3+2pin,x=(5pi)/3+2pin

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4sin^2(x)=5-4cos(x)

4 sin^{2} (x) = 5 - 4 cos (x)

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

4 sin^{2} (x) = 5 - 4 cos (x)

Subtract

5 - 4 cos (x)

from both sides

4 sin^{2} (x) - 5 + 4 cos (x) = 0

Rewrite using trig identities

- 1 + 4 cos (x) - 4 cos^{2} (x) = 0

Solve by substitution

cos (x) = \frac{1}{2}

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sec (\frac{5 π}{3})

2 sin (3 x) - 3 = 0

- sin (0)

sec (\frac{5 π}{4})

cot (\frac{11 π}{6})

What is the general solution for 4sin^2(x)=5-4cos(x) ?
The general solution for 4sin^2(x)=5-4cos(x) is x= pi/3+2pin,x=(5pi)/3+2pin