What is the general solution for 6cos^2(x)-5sin(x)-2=0 ?

The general solution for 6cos^2(x)-5sin(x)-2=0 is x= pi/6+2pin,x=(5pi)/6+2pin

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6cos^2(x)-5sin(x)-2=0

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

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

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

Rewrite using trig identities

4 - 5 sin (x) - 6 sin^{2} (x) = 0

Solve by substitution

sin (x) = - \frac{4}{3}, sin (x) = \frac{1}{2}

sin (x) = - \frac{4}{3} :

No Solution

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sec (θ) = - \frac{7}{4}

arctan (x) = \infty

r = a (1 - sin (x))

(cos (θ)) (cos (θ)) + 1 = (sin (θ)) (sin (θ))

1 + 4 tan^{2} (θ) = sec^{2} (θ)

What is the general solution for 6cos^2(x)-5sin(x)-2=0 ?
The general solution for 6cos^2(x)-5sin(x)-2=0 is x= pi/6+2pin,x=(5pi)/6+2pin