What is the general solution for 4cos^2(x)-18cos(x)-10=0 ?

The general solution for 4cos^2(x)-18cos(x)-10=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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4cos^2(x)-18cos(x)-10=0

4 cos^{2} (x) - 18 cos (x) - 10 = 0

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

Solution steps

4 cos^{2} (x) - 18 cos (x) - 10 = 0

Solve by substitution

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

cos (x) = 5 :

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

25 sin (θ) - 1.5 cos (θ) = 20

sin (\frac{2 θ}{3}) = \frac{1}{2}, 0 \leq θ \leq 2 π

1 - sin^{2} (x) = e^{\frac{1}{2} l n (1 - c o s^{2} (x))}

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

cos (C) = \frac{3}{4}

What is the general solution for 4cos^2(x)-18cos(x)-10=0 ?
The general solution for 4cos^2(x)-18cos(x)-10=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin