What is the general solution for 6-24cos^2(t)=0 ?

The general solution for 6-24cos^2(t)=0 is t= pi/3+2pin,t=(5pi)/3+2pin,t=(2pi)/3+2pin,t=(4pi)/3+2pin

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6-24cos^2(t)=0

6 - 24 cos^{2} (t) = 0

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

Solution steps

6 - 24 cos^{2} (t) = 0

Solve by substitution

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

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

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

Combine all the solutions

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

sin^{2} (x) - sin (x) = 2, 0 \leq x \leq 2 π

tan (x) = - 2, 0 \leq x \leq 2 π

7 sin (x) = 0

cos (θ) = \frac{33}{55}

\frac{120}{sin ( x )} = \frac{30}{sin ( 8 )}

What is the general solution for 6-24cos^2(t)=0 ?
The general solution for 6-24cos^2(t)=0 is t= pi/3+2pin,t=(5pi)/3+2pin,t=(2pi)/3+2pin,t=(4pi)/3+2pin