What is the general solution for 4sin^2(x)=4cos(x)+1 ?

The general solution for 4sin^2(x)=4cos(x)+1 is x= pi/3+2pin,x=(5pi)/3+2pin

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4sin^2(x)=4cos(x)+1

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

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

Solution steps

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

Subtract

4 cos (x) + 1

from both sides

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

Rewrite using trig identities

3 - 4 cos (x) - 4 cos^{2} (x) = 0

Solve by substitution

cos (x) = - \frac{3}{2}, cos (x) = \frac{1}{2}

cos (x) = - \frac{3}{2} :

No Solution

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

2 tan^{2} (x) + 3 tan (x) - 2 = 0

sin^{2} (2 x) - \frac{1}{2 3} sin (4 x) = \frac{1}{2}

x, sin (x + x y) = 0

sin (x) = - 3 cos (x)

- 2 sin^{2} (θ) + cos (θ) + 8 = 6

What is the general solution for 4sin^2(x)=4cos(x)+1 ?
The general solution for 4sin^2(x)=4cos(x)+1 is x= pi/3+2pin,x=(5pi)/3+2pin