What is the general solution for cos(x+3)=cos(x) ?

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

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cos(x+3)=cos(x)

cos (x + 3) = cos (x)

x = 2 πn - \frac{3}{2}, x = - \frac{3}{2} + π + 2 πn

Solution steps

cos (x + 3) = cos (x)

Subtract

cos (x)

from both sides

cos (x + 3) - cos (x) = 0

Rewrite using trig identities

- 2 sin (\frac{3}{2}) sin (\frac{2 x + 3}{2}) = 0

Divide both sides by

- 2 sin (\frac{3}{2})

sin (\frac{2 x + 3}{2}) = 0

General solutions for

sin (\frac{2 x + 3}{2}) = 0

\frac{2 x + 3}{2} = 0 + 2 πn, \frac{2 x + 3}{2} = π + 2 πn

Solve

\frac{2 x + 3}{2} = 0 + 2 πn : x = 2 πn - \frac{3}{2}

Solve

\frac{2 x + 3}{2} = π + 2 πn : x = - \frac{3}{2} + π + 2 πn

x = 2 πn - \frac{3}{2}, x = - \frac{3}{2} + π + 2 πn

sin (x) - cos (x) = \frac{1}{3}, sin (2 x)

- 9 cos (θ) = \frac{3 2}{2}

sec (a) = 1 + tan (a)

arctan (θ) = \frac{2}{2 3}

3 sin (x) = + sin (x)

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