What is the general solution for 2cos^2(w)+3cos(w)+1=0 ?

The general solution for 2cos^2(w)+3cos(w)+1=0 is w=(2pi)/3+2pin,w=(4pi)/3+2pin,w=pi+2pin

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2cos^2(w)+3cos(w)+1=0

2 cos^{2} (w) + 3 cos (w) + 1 = 0

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

Solution steps

2 cos^{2} (w) + 3 cos (w) + 1 = 0

Solve by substitution

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

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

cos (w) = - 1 : w = π + 2 πn

Combine all the solutions

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

cos (3 x) + sin (3 x) = 1

3 csc (2 x) = - 2

cos (3 x) = 4 cos (3 x) - 3 cos (x)

8 arctan (x) = 2 π

sin^{2} (θ) - 1 = cos^{2} (θ)

What is the general solution for 2cos^2(w)+3cos(w)+1=0 ?
The general solution for 2cos^2(w)+3cos(w)+1=0 is w=(2pi)/3+2pin,w=(4pi)/3+2pin,w=pi+2pin