What is the general solution for 2sin^2(x)-5sin(x)=3 ?

The general solution for 2sin^2(x)-5sin(x)=3 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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2sin^2(x)-5sin(x)=3

2 sin^{2} (x) - 5 sin (x) = 3

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

Solution steps

2 sin^{2} (x) - 5 sin (x) = 3

Solve by substitution

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

sin (x) = 3 :

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

cos (8 x) - cos (2 x) = sin (5 x)

tan (x) = - \frac{1}{5}

2 + 2 cos (x) = 0

2 sin (θ) sec (θ) = 4 sin (θ)

sec (x - \frac{π}{7}) cos (x - \frac{π}{7}) = sin (x - \frac{π}{7})

What is the general solution for 2sin^2(x)-5sin(x)=3 ?
The general solution for 2sin^2(x)-5sin(x)=3 is x=(7pi)/6+2pin,x=(11pi)/6+2pin