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=(2pi)/3+2pin,x=(4pi)/3+2pin

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

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

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

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

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

No Solution

Combine all the solutions

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

\frac{sin ^{22} ( a )}{sin ^{2} ( a )} = 4 - 4 sin^{2} (a)

tan^{3} (x) = 2

sin^{3} (x) = 3 sin (x)

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

1 + sin (2 a) = sin^{2} (a)

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=(2pi)/3+2pin,x=(4pi)/3+2pin