What is the general solution for 2cos^2(x)-3cos(x)-5=0 ?

The general solution for 2cos^2(x)-3cos(x)-5=0 is x=pi+2pin

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2cos^2(x)-3cos(x)-5=0

2 cos^{2} (x) - 3 cos (x) - 5 = 0

x = π + 2 πn

Solution steps

2 cos^{2} (x) - 3 cos (x) - 5 = 0

Solve by substitution

cos (x) = \frac{5}{2}, cos (x) = - 1

cos (x) = \frac{5}{2} :

No Solution

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = π + 2 πn

cos (2 x) = - cos (x), 0 \leq x \leq 2 π

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

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

3 csc (2 x) = - 2

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

What is the general solution for 2cos^2(x)-3cos(x)-5=0 ?
The general solution for 2cos^2(x)-3cos(x)-5=0 is x=pi+2pin