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

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

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

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

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) - cos (2 x) = 1

Subtract

1

from both sides

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

tan (θ) = \frac{1}{2}

- cos (x) - sin (x) = 1

sin (2 x) = sin (0.5 x)

2 sin (2 x + 15) = \frac{1}{2}

sin^{2} (x) - 2 cos^{4} (x) = 0

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