What is the general solution for cos(x)-1=cos(2x) ?

The general solution for cos(x)-1=cos(2x) is x= pi/2+2pin,x=(3pi)/2+2pin,x= pi/3+2pin,x=(5pi)/3+2pin

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cos(x)-1=cos(2x)

cos (x) - 1 = cos (2 x)

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

cos (x) - 1 = cos (2 x)

Subtract

cos (2 x)

from both sides

cos (x) - 1 - cos (2 x) = 0

Rewrite using trig identities

cos (x) - 2 cos^{2} (x) = 0

Solve by substitution

cos (x) = 0, cos (x) = \frac{1}{2}

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

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sin (x + \frac{π}{4}) = \frac{2}{2}

tan (θ) = 2.4

sin (x) (2 sin (x) - 1) = 0

cos (x) = \frac{1}{8}

tan (θ) = 1.5

What is the general solution for cos(x)-1=cos(2x) ?
The general solution for cos(x)-1=cos(2x) is x= pi/2+2pin,x=(3pi)/2+2pin,x= pi/3+2pin,x=(5pi)/3+2pin