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

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

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cos(θ)-1=cos(2θ)

cos (θ) - 1 = cos (2 θ)

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

Solution steps

cos (θ) - 1 = cos (2 θ)

Subtract

cos (2 θ)

from both sides

cos (θ) - 1 - cos (2 θ) = 0

Rewrite using trig identities

cos (θ) - 2 cos^{2} (θ) = 0

Solve by substitution

cos (θ) = 0, cos (θ) = \frac{1}{2}

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

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

Combine all the solutions

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

5 tan (x) = 9 sin (x)

x, sin (\frac{π x}{4}) = y - 1

sin (θ) = \frac{12}{37}

8 tan (\frac{θ}{2}) + 8 cos (θ) tan (\frac{θ}{2}) = 1

m (0) = sin (2 x) + 2

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