What is the general solution for 6sin^2(θ)-17sin(θ)+14=-4sin(θ)+9 ?

The general solution for 6sin^2(θ)-17sin(θ)+14=-4sin(θ)+9 is θ= pi/6+2pin,θ=(5pi)/6+2pin

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6sin^2(θ)-17sin(θ)+14=-4sin(θ)+9

6 sin^{2} (θ) - 17 sin (θ) + 14 = - 4 sin (θ) + 9

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Solution steps

6 sin^{2} (θ) - 17 sin (θ) + 14 = - 4 sin (θ) + 9

Solve by substitution

sin (θ) = \frac{5}{3}, sin (θ) = \frac{1}{2}

sin (θ) = \frac{5}{3} :

No Solution

sin (θ) = \frac{1}{2} : θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Combine all the solutions

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

sin (x) - 2 sin (x) cos (x) = 0, 0 \leq x \leq 2 π

cos (x + π) - cos (x) - 1 = 0

sin (x) = \frac{15}{17}

2 cos (x) - sec (x) = 1

cos (x) tan (x) = 5 tan (x)

What is the general solution for 6sin^2(θ)-17sin(θ)+14=-4sin(θ)+9 ?
The general solution for 6sin^2(θ)-17sin(θ)+14=-4sin(θ)+9 is θ= pi/6+2pin,θ=(5pi)/6+2pin