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

The general solution for 6sin^2(x)-5cos(x)-2=0 is x= pi/3+2pin,x=(5pi)/3+2pin

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

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

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

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

No Solution

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sin (θ) + cos (θ) = \frac{3}{5}

sec (x) - 4 = 0

csc (θ) - cot^{2} (θ) + 1 = 0

sin (x - 4 0^{\circ}) = 1

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

What is the general solution for 6sin^2(x)-5cos(x)-2=0 ?
The general solution for 6sin^2(x)-5cos(x)-2=0 is x= pi/3+2pin,x=(5pi)/3+2pin