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

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

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cos(2x)+1=cos(x)

cos (2 x) + 1 = cos (x)

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

Solution steps

cos (2 x) + 1 = cos (x)

Subtract

cos (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

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

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

Combine all the solutions

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

4 cos (x) + 1 = 0

2 cot^{2} (x) + csc^{2} (x) - 2 = 0

cos^{2} (x) = \frac{1}{2} sin (2 x)

3 cot (θ) + 5 = 0

x, h = g

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