What is the general solution for 4cos^3(x)-7cos(x)-3=0 ?

The general solution for 4cos^3(x)-7cos(x)-3=0 is x=pi+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin

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4cos^3(x)-7cos(x)-3=0

4 cos^{3} (x) - 7 cos (x) - 3 = 0

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

Solution steps

4 cos^{3} (x) - 7 cos (x) - 3 = 0

Solve by substitution

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

cos (x) = - 1 : x = π + 2 πn

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

cos (x) = \frac{3}{2} :

No Solution

Combine all the solutions

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

\frac{sin ( θ )}{1.3} = \frac{sin ( 12 5 ^{\circ} )}{2.8519}

cot^{2} (θ) = \frac{1}{3}

x, y^{3} - sin^{2} (x) = 1

- cos (2 x) - 4 sin^{2} (x) + 2 = 0

sec (θ) - 2 cos (θ) = 0

What is the general solution for 4cos^3(x)-7cos(x)-3=0 ?
The general solution for 4cos^3(x)-7cos(x)-3=0 is x=pi+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin