What is the general solution for cos^4(x)= 3/8+1/2 cos^2(x)+1/8 cos^4(x) ?

The general solution for cos^4(x)= 3/8+1/2 cos^2(x)+1/8 cos^4(x) is x=2pin,x=pi+2pin

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cos^4(x)= 3/8+1/2 cos^2(x)+1/8 cos^4(x)

cos^{4} (x) = \frac{3}{8} + \frac{1}{2} cos^{2} (x) + \frac{1}{8} cos^{4} (x)

x = 2 πn, x = π + 2 πn

Solution steps

cos^{4} (x) = \frac{3}{8} + \frac{1}{2} cos^{2} (x) + \frac{1}{8} cos^{4} (x)

Solve by substitution

cos (x) = i \frac{3}{7}, cos (x) = - i \frac{3}{7}, cos (x) = 1, cos (x) = - 1

cos (x) = i \frac{3}{7} :

No Solution

cos (x) = - i \frac{3}{7} :

No Solution

cos (x) = 1 : x = 2 πn

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

sin (2 x) = 5 cos (x)

sin (a) = 0.4848

sin^{2} (x) = 2 cos^{4} (x)

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

i, x sin^{2} (x) = cos^{2} (x)

What is the general solution for cos^4(x)= 3/8+1/2 cos^2(x)+1/8 cos^4(x) ?
The general solution for cos^4(x)= 3/8+1/2 cos^2(x)+1/8 cos^4(x) is x=2pin,x=pi+2pin