What is the general solution for 4cos^2(x)=3 ?

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

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4cos^2(x)=3

4 cos^{2} (x) = 3

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

Solution steps

4 cos^{2} (x) = 3

Solve by substitution

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

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

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

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

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

csc (x) = 0

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

cos (x) + 3 = - cos (x)

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

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