What is the general solution for 2cos^2(θ)+2sin(θ)-12=9sin(θ)-7 ?

The general solution for 2cos^2(θ)+2sin(θ)-12=9sin(θ)-7 is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

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2cos^2(θ)+2sin(θ)-12=9sin(θ)-7

2 cos^{2} (θ) + 2 sin (θ) - 12 = 9 sin (θ) - 7

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

Solution steps

2 cos^{2} (θ) + 2 sin (θ) - 12 = 9 sin (θ) - 7

Subtract

9 sin (θ) - 7

from both sides

2 cos^{2} (θ) - 7 sin (θ) - 5 = 0

Rewrite using trig identities

- 3 - 2 sin^{2} (θ) - 7 sin (θ) = 0

Solve by substitution

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

sin (θ) = - 3 :

No Solution

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

Combine all the solutions

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

2 csc^{2} (x) + cot^{2} (x) - 3 = 0

tan (x) = 0.095

θ, x = tan^{2} (θ)

sin^{2} (x) cos^{2} (x) = 1

- 1 = - 4 sec (x) - sec^{2} (x) - 5

What is the general solution for 2cos^2(θ)+2sin(θ)-12=9sin(θ)-7 ?
The general solution for 2cos^2(θ)+2sin(θ)-12=9sin(θ)-7 is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin