What is the general solution for 36cos^2(x)-9=0 ?

The general solution for 36cos^2(x)-9=0 is x= pi/3+2pin,x=(5pi)/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin

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36cos^2(x)-9=0

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

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

Solution steps

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

Solve by substitution

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

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

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

Combine all the solutions

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

sin (x) = \frac{5}{6}

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

csc (θ) = 4

2 sin (2 θ) = - 2

2 sin (2 x) = 2

What is the general solution for 36cos^2(x)-9=0 ?
The general solution for 36cos^2(x)-9=0 is x= pi/3+2pin,x=(5pi)/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin