What is the general solution for (1-sin^2(x))*2-3sin(x)=0 ?

The general solution for (1-sin^2(x))*2-3sin(x)=0 is x= pi/6+2pin,x=(5pi)/6+2pin

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(1-sin^2(x))*2-3sin(x)=0

(1 - sin^{2} (x)) \cdot 2 - 3 sin (x) = 0

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

Solution steps

(1 - sin^{2} (x)) \cdot 2 - 3 sin (x) = 0

Solve by substitution

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

sin (x) = - 2 :

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

sin (\frac{θ}{2}) = sin (θ)

2 tan (x) = 1

2 tan (x) = 3

4 sin^{2} (x) = 2 sin (x) + 6

4 sin (x) - 1 = 0

What is the general solution for (1-sin^2(x))*2-3sin(x)=0 ?
The general solution for (1-sin^2(x))*2-3sin(x)=0 is x= pi/6+2pin,x=(5pi)/6+2pin