What is the general solution for cos^4(x)= 1/16 ?

The general solution for cos^4(x)= 1/16 is x= pi/3+2pin,x=(5pi)/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin

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cos^4(x)= 1/16

cos^{4} (x) = \frac{1}{16}

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Solution steps

cos^{4} (x) = \frac{1}{16}

Solve by substitution

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

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

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

No Solution

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

No Solution

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

w, P = 4 (\frac{Y}{P sin ( w )})

tan (2 θ) = \frac{500}{350 - 75}

sec (a) = - 2

tan^{2} (γ) + 1 = cos^{2} (γ)

sin^{2} (x) + 8 sin (x) - 9 = 0

What is the general solution for cos^4(x)= 1/16 ?
The general solution for cos^4(x)= 1/16 is x= pi/3+2pin,x=(5pi)/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin