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

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

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cos(2t)+cos(t)=0

cos (2 t) + cos (t) = 0

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

Solution steps

cos (2 t) + cos (t) = 0

Rewrite using trig identities

2 cos (\frac{3 t}{2}) cos (\frac{t}{2}) = 0

Solving each part separately

cos (\frac{3 t}{2}) = 0 or cos (\frac{t}{2}) = 0

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

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

Combine all the solutions

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

Merge Overlapping Intervals

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

\frac{π}{6} = sin (3 x)

tan (x) = 3 tan (\frac{1}{2} x)

cos (t) = \frac{- 5}{13}, \frac{1}{2} π < t < π

31.91 cos (x) = 20.48

7 sin (x) + 7 sin (x) tan (x) = 0

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