What is the general solution for 4cos(x)=cos^3(x) ?

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

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4cos(x)=cos^3(x)

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

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

Solution steps

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

Solve by substitution

cos (x) = 0, cos (x) = - 2, cos (x) = 2

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

cos (x) = - 2 :

No Solution

cos (x) = 2 :

No Solution

Combine all the solutions

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

cos^{2} (a) = \frac{3}{5 sin ( a )}

3 cos (x) = 2 sec (x) - 5

sin (\frac{a}{2}) = (\frac{1}{2}) sin (a)

cos (\frac{x}{2}) = cos (x) + 1

d = \frac{sin ^{4} ( x ) - cos ^{2} ( x ) + 5}{4 \cdot cos ^{2} ( x )}

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