What is the general solution for 4sin^2(x)-4cos(x)-1=0 ?

The general solution for 4sin^2(x)-4cos(x)-1=0 is x= pi/3+2pin,x=(5pi)/3+2pin

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

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

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

Solution steps

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

3 cos^{2} (x) + 2 cos (x) - 8 = 0

tan (a) + sec (a) = \frac{3}{2}

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

cos (2 x + 3) = 0

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

What is the general solution for 4sin^2(x)-4cos(x)-1=0 ?
The general solution for 4sin^2(x)-4cos(x)-1=0 is x= pi/3+2pin,x=(5pi)/3+2pin