What is the general solution for cos^2(x)-cos(x)=0.75 ?

The general solution for cos^2(x)-cos(x)=0.75 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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cos^2(x)-cos(x)=0.75

cos^{2} (x) - cos (x) = 0.75

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

Solution steps

cos^{2} (x) - cos (x) = 0.75

Solve by substitution

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

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

No Solution

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

Combine all the solutions

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

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

2 tan (x) = tan (x) tan (x)

\frac{2 tan ( x )}{1 - tan ^{2} ( x )} = 3

tan (x) = \frac{59}{56}

cos (θ) = \frac{5}{5 2}

What is the general solution for cos^2(x)-cos(x)=0.75 ?
The general solution for cos^2(x)-cos(x)=0.75 is x=(2pi)/3+2pin,x=(4pi)/3+2pin