What is the general solution for cos^6(x)=-cos^2(x) ?

The general solution for cos^6(x)=-cos^2(x) is x= pi/2+2pin,x=(3pi)/2+2pin

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cos^6(x)=-cos^2(x)

cos^{6} (x) = - cos^{2} (x)

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

Solution steps

cos^{6} (x) = - cos^{2} (x)

Solve by substitution

cos (x) = 0, cos (x) = \frac{1}{2} + \frac{1}{2} i, cos (x) = - \frac{1}{2} - \frac{1}{2} i, cos (x) = - \frac{1}{2} + \frac{1}{2} i, cos (x) = \frac{1}{2} - \frac{1}{2} i

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

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

No Solution

cos (x) = - \frac{1}{2} - \frac{1}{2} i :

No Solution

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

No Solution

cos (x) = \frac{1}{2} - \frac{1}{2} i :

No Solution

Combine all the solutions

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

2 sin^{3} (x) - 5 sin^{2} (x) + 2 sin (x) = 0

\frac{cos ^{2} ( a ) - 3 cos ( a ) + 2}{sin ^{2} ( a )} = 1

\frac{sin ( x ) - ( 2 )}{2} = 0

cos (2 x) = 5 - 6 cos^{2} (x)

cos^{4} (x) = 0.37

What is the general solution for cos^6(x)=-cos^2(x) ?
The general solution for cos^6(x)=-cos^2(x) is x= pi/2+2pin,x=(3pi)/2+2pin