What is the general solution for 7cos(θ)=7cos(2θ) ?

The general solution for 7cos(θ)=7cos(2θ) is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin,θ=2pin

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7cos(θ)=7cos(2θ)

7 cos (θ) = 7 cos (2 θ)

θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn, θ = 2 πn

Solution steps

7 cos (θ) = 7 cos (2 θ)

Subtract

7 cos (2 θ)

from both sides

7 cos (θ) - 7 cos (2 θ) = 0

Rewrite using trig identities

- (- 1 + 2 cos^{2} (θ)) \cdot 7 + 7 cos (θ) = 0

Solve by substitution

cos (θ) = - \frac{1}{2}, cos (θ) = 1

cos (θ) = - \frac{1}{2} : θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

cos (θ) = 1 : θ = 2 πn

Combine all the solutions

θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn, θ = 2 πn

3 cos (2 x) = 3 cos (x)

sin^{2} (2 x) = 3 cos^{2} (2 x)

- 2 sin (θ) = 2 sin (2 θ)

cos (θ) = \frac{π}{2}

2 sin (4 x) + 3 = 0

What is the general solution for 7cos(θ)=7cos(2θ) ?
The general solution for 7cos(θ)=7cos(2θ) is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin,θ=2pin