What is the general solution for 4cos^2(β)-4cos(β)=3 ?

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

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4cos^2(β)-4cos(β)=3

4 cos^{2} (β) - 4 cos (β) = 3

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

Solution steps

4 cos^{2} (β) - 4 cos (β) = 3

Solve by substitution

cos (β) = \frac{3}{2}, cos (β) = - \frac{1}{2}

cos (β) = \frac{3}{2} :

No Solution

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

Combine all the solutions

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

x, cot (x) = 1

sin^{4} (x) + cos^{4} (x) = \frac{5}{8}

0 = \frac{1}{9} sin (9 t)

tan (x) = \frac{3}{3}

9 cot^{2} (θ) - 25 = 0

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