What is the general solution for cos(x)-cos(x+pi/4)=0 ?

The general solution for cos(x)-cos(x+pi/4)=0 is x=2pin-pi/8 ,x=(7pi)/8+2pin

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cos(x)-cos(x+pi/4)=0

cos (x) - cos (x + \frac{π}{4}) = 0

x = 2 πn - \frac{π}{8}, x = \frac{7 π}{8} + 2 πn

Solution steps

cos (x) - cos (x + \frac{π}{4}) = 0

Rewrite using trig identities

2 - 2 sin (\frac{8 x + π}{8}) = 0

Divide both sides by

2 - 2

sin (\frac{8 x + π}{8}) = 0

General solutions for

sin (\frac{8 x + π}{8}) = 0

\frac{8 x + π}{8} = 0 + 2 πn, \frac{8 x + π}{8} = π + 2 πn

Solve

\frac{8 x + π}{8} = 0 + 2 πn : x = 2 πn - \frac{π}{8}

Solve

\frac{8 x + π}{8} = π + 2 πn : x = \frac{7 π}{8} + 2 πn

x = 2 πn - \frac{π}{8}, x = \frac{7 π}{8} + 2 πn

cos (x) = 0.7597

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cos (x) = \frac{280}{2000}

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x, T (6) = 3.15 cos (\frac{π}{6} x) + 19.15

What is the general solution for cos(x)-cos(x+pi/4)=0 ?
The general solution for cos(x)-cos(x+pi/4)=0 is x=2pin-pi/8 ,x=(7pi)/8+2pin