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=(7pi)/6+2pin,x=(11pi)/6+2pin

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

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

x = \frac{7 π}{6} + 2 πn, x = \frac{11 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{1}{2}, sin (x) = \frac{4}{3}

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

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

No Solution

Combine all the solutions

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

\frac{tan ^{2} ( b ) + 1}{tan ( b )} = csc^{2} (b)

x, r + s + 6 t = cos (2 x + y)

\frac{tan ^{2} ( b ) + 1}{( tan ( x ) )} = csc^{2} (b)

sin (x) + sin^{2} (\frac{x}{2}) = \frac{1}{2}

sin^{5} (x) + sin^{3} (x) = 0

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=(7pi)/6+2pin,x=(11pi)/6+2pin