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

The general solution for 4cos^2(x)-3=0,0<= x<= 2pi is x= pi/6 ,x=(11pi)/6 ,x=(5pi)/6 ,x=(7pi)/6

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4cos^2(x)-3=0,0<= x<= 2pi

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

x = \frac{π}{6}, x = \frac{11 π}{6}, x = \frac{5 π}{6}, x = \frac{7 π}{6}

Solution steps

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

Solve by substitution

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

cos (x) = \frac{3}{2}, 0 \leq x \leq 2 π : x = \frac{π}{6}, x = \frac{11 π}{6}

cos (x) = - \frac{3}{2}, 0 \leq x \leq 2 π : x = \frac{5 π}{6}, x = \frac{7 π}{6}

Combine all the solutions

x = \frac{π}{6}, x = \frac{11 π}{6}, x = \frac{5 π}{6}, x = \frac{7 π}{6}

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

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

12 cos^{2} (x) - 9 = 0

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

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

What is the general solution for 4cos^2(x)-3=0,0<= x<= 2pi ?
The general solution for 4cos^2(x)-3=0,0<= x<= 2pi is x= pi/6 ,x=(11pi)/6 ,x=(5pi)/6 ,x=(7pi)/6