What is the general solution for 7cos^3(x)=7cos(x) ?

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

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7cos^3(x)=7cos(x)

7 cos^{3} (x) = 7 cos (x)

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

Solution steps

7 cos^{3} (x) = 7 cos (x)

Solve by substitution

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

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

cos (x) = - 1 : x = π + 2 πn

cos (x) = 1 : x = 2 πn

Combine all the solutions

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

0 = - 2 sin (x)

cos (2 θ) - 3 cos (θ) = 0

tan (x) + sec (x) = 0

cos (θ) = \frac{3}{2}

cos^{2} (θ) + 2 sin (θ) cos (θ) - sin^{2} (θ) = 0

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