What is the general solution for cos^5(x)=cos(x) ?

The general solution for cos^5(x)=cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin,x=pi+2pin,x=2pin

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cos^5(x)=cos(x)

cos^{5} (x) = cos (x)

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

Solution steps

cos^{5} (x) = cos (x)

Solve by substitution

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

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

cos (x) = i :

No Solution

cos (x) = - i :

No Solution

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

tan (x) = (\frac{1.8}{3.6})

sec (x + 3 0^{\circ}) = 2

y, arccos (\frac{y}{2}) = 5 lo g_{10} (\frac{x}{5})

sin^{22} (x) = \frac{1}{4}

3 sin (2 x) - cos (x) = 0

What is the general solution for cos^5(x)=cos(x) ?
The general solution for cos^5(x)=cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin,x=pi+2pin,x=2pin