What is the general solution for cos^2(x)= 1/4 ,0<= x<= 2pi ?

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

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cos^2(x)= 1/4 ,0<= x<= 2pi

cos^{2} (x) = \frac{1}{4}, 0 \leq x \leq 2 π

x = \frac{π}{3}, x = \frac{5 π}{3}, x = \frac{2 π}{3}, x = \frac{4 π}{3}

Solution steps

cos^{2} (x) = \frac{1}{4}, 0 \leq x \leq 2 π

Solve by substitution

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

cos (x) = \frac{1}{2}, 0 \leq x \leq 2 π : x = \frac{π}{3}, x = \frac{5 π}{3}

cos (x) = - \frac{1}{2}, 0 \leq x \leq 2 π : x = \frac{2 π}{3}, x = \frac{4 π}{3}

Combine all the solutions

x = \frac{π}{3}, x = \frac{5 π}{3}, x = \frac{2 π}{3}, x = \frac{4 π}{3}

sin (θ) = - \frac{4}{9}

- sin (y) = 0

0 = 2 + 4 sin (θ)

cos (x) = \frac{71}{81}

2 sin^{2} (2 x) - sin (2 x) - 3 = 0

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