What is the general solution for solvefor x,cos(2x)=-cos(x) ?

The general solution for solvefor x,cos(2x)=-cos(x) is x= pi/3+(4pin)/3 ,x=pi+(4pin)/3

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Solve for x cos(2x)=-cos(x)

solve for

x, cos (2 x) = - cos (x)

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

Solution steps

cos (2 x) = - cos (x)

Subtract

- cos (x)

from both sides

cos (2 x) + cos (x) = 0

Rewrite using trig identities

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

Solving each part separately

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

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

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

Combine all the solutions

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

Merge Overlapping Intervals

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

sin (\frac{( 2 π )}{3})

sin (x) = \frac{4}{5}, cos (x) = \frac{3}{5}

\frac{50}{( tan ( 5 3 ^{\circ} ) )}

cos (\frac{( 3 π )}{2})

sin (\frac{( 3 π )}{4})

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