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

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

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cos^3(x)-3cos(x)=3cos(x)sin(x)

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

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

Solution steps

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

Subtract

3 cos (x) sin (x)

from both sides

cos^{3} (x) - 3 cos (x) - 3 cos (x) sin (x) = 0

Factor

cos^{3} (x) - 3 cos (x) - 3 cos (x) sin (x) : cos (x) (cos^{2} (x) - 3 - 3 sin (x))

cos (x) (cos^{2} (x) - 3 - 3 sin (x)) = 0

Solving each part separately

cos (x) = 0 or cos^{2} (x) - 3 - 3 sin (x) = 0

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

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

Combine all the solutions

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

sin (x) = 0.88

tan (b) = 1

5 cos^{2} (θ) - 1 = cos^{2} (θ)

cos (x) = \frac{2}{9}

x, tan (x) + tan (y) = 1

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