What is the general solution for 2-8cos^2(t)=0 ?

The general solution for 2-8cos^2(t)=0 is t= pi/3+2pin,t=(5pi)/3+2pin,t=(2pi)/3+2pin,t=(4pi)/3+2pin

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2-8cos^2(t)=0

2 - 8 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

2 - 8 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

cos (θ) + 1 = 1

9 cos (x) tan (x) = - 8 tan (x)

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

sin (x) cos (x) = - 9 cos (x)

5 tan (θ) - 7 = 0

What is the general solution for 2-8cos^2(t)=0 ?
The general solution for 2-8cos^2(t)=0 is t= pi/3+2pin,t=(5pi)/3+2pin,t=(2pi)/3+2pin,t=(4pi)/3+2pin