What is the general solution for 2cos^2(x)-cos(x)-3=0 ?

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

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2cos^2(x)-cos(x)-3=0

2 cos^{2} (x) - cos (x) - 3 = 0

x = π + 2 πn

Solution steps

2 cos^{2} (x) - cos (x) - 3 = 0

Solve by substitution

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

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

No Solution

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = π + 2 πn

arcsin (x) = \frac{π}{7}

2 sin (2 θ) = - 1

sin (4 θ) = - \frac{2 3}{3}

cos (2 x) + 5 sin (x) + 2 = 0

2 sin^{2} (θ) - 3 cos (θ) = 3

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