What is the general solution for 5sqrt(cos(2t))cos(t)=0 ?

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

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5sqrt(cos(2t))cos(t)=0

5 cos (2 t) cos (t) = 0

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

Solution steps

5 cos (2 t) cos (t) = 0

Solving each part separately

cos (2 t) = 0 or cos (t) = 0

cos (2 t) = 0 : t = \frac{π}{4} + πn, t = \frac{3 π}{4} + πn

cos (t) = 0 : t = \frac{π}{2} + 2 πn, t = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

Since the equation is undefined for:

\frac{π}{2} + 2 πn, \frac{3 π}{2} + 2 πn

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

k, 6 (- cos (\frac{k}{2}) + 1) = 1.5

tan (x) sec (x) = 2 tan (x)

tan (x) = \frac{5.1}{10.5}

tan (x) = 3, 0 \leq x < 2 π

3 tan^{2} (x) + 4 tan (x) - 3 = 0

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