What is the general solution for 2sin^2(x)-13sin(x)+6=0 ?

The general solution for 2sin^2(x)-13sin(x)+6=0 is x= pi/6+2pin,x=(5pi)/6+2pin

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2sin^2(x)-13sin(x)+6=0

2 sin^{2} (x) - 13 sin (x) + 6 = 0

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

Solution steps

2 sin^{2} (x) - 13 sin (x) + 6 = 0

Solve by substitution

sin (x) = 6, sin (x) = \frac{1}{2}

sin (x) = 6 :

No Solution

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

Combine all the solutions

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

2 tan (θ) + 3 = 0

tan (x) = \frac{4}{6}

cos (2 x) = - 2 cos^{2} (x)

cos^{2} (θ) + 2 cos (θ) = 0

tan (x) = sec (x) - 3

What is the general solution for 2sin^2(x)-13sin(x)+6=0 ?
The general solution for 2sin^2(x)-13sin(x)+6=0 is x= pi/6+2pin,x=(5pi)/6+2pin