What is the general solution for -2cos^2(x)-9sin(x)-3=0 ?

The general solution for -2cos^2(x)-9sin(x)-3=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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-2cos^2(x)-9sin(x)-3=0

- 2 cos^{2} (x) - 9 sin (x) - 3 = 0

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

Solution steps

- 2 cos^{2} (x) - 9 sin (x) - 3 = 0

Rewrite using trig identities

- 5 + 2 sin^{2} (x) - 9 sin (x) = 0

Solve by substitution

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

sin (x) = 5 :

No Solution

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

Combine all the solutions

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

sin (2 x) = - \frac{2 6}{7}

tan (6 x) - 3 tan (3 x) = 0

sin (a) = \frac{2}{5}

cos^{2} (θ) - cos (θ) - 1 = 0

3 cot^{2} (x) - 4 csc (x) = 1

What is the general solution for -2cos^2(x)-9sin(x)-3=0 ?
The general solution for -2cos^2(x)-9sin(x)-3=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin