What is the general solution for cos(x+pi/6)-1=cos(x-pi/6) ?

The general solution for cos(x+pi/6)-1=cos(x-pi/6) is x=(3pi)/2+2pin

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cos(x+pi/6)-1=cos(x-pi/6)

cos (x + \frac{π}{6}) - 1 = cos (x - \frac{π}{6})

x = \frac{3 π}{2} + 2 πn

Solution steps

cos (x + \frac{π}{6}) - 1 = cos (x - \frac{π}{6})

Rewrite using trig identities

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

Subtract

\frac{3}{2} cos (x) + \frac{1}{2} sin (x)

from both sides

- sin (x) - 1 = 0

Move

1

to the right side

- sin (x) = 1

Divide both sides by

- 1

sin (x) = - 1

General solutions for

sin (x) = - 1

x = \frac{3 π}{2} + 2 πn

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

2 sin (θ) = cos (2 θ)

tan (θ) = \frac{4}{- 4}

sin (x) = \frac{2}{7}

sin (θ) cos (θ) + sin (θ) = 0

What is the general solution for cos(x+pi/6)-1=cos(x-pi/6) ?
The general solution for cos(x+pi/6)-1=cos(x-pi/6) is x=(3pi)/2+2pin