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

The general solution for 2sin(x)-3sin(x)+1=0 is x= pi/2+2pin

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2sin(x)-3sin(x)+1=0

2 sin (x) - 3 sin (x) + 1 = 0

x = \frac{π}{2} + 2 πn

Solution steps

2 sin (x) - 3 sin (x) + 1 = 0

Simplify

2 sin (x) - 3 sin (x) + 1 : - sin (x) + 1

- sin (x) + 1 = 0

Move

1

to the right side

- sin (x) = - 1

Divide both sides by

- 1

sin (x) = 1

General solutions for

sin (x) = 1

x = \frac{π}{2} + 2 πn

2 sin (x) (sin (x) - 1) = 3 cos^{2} (x)

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

sin (x) cos^{2} (x) = sin (x), 0 \leq x \leq 2 π

2 \cdot cos (4 x) - 1 = 0

2 cos^{2} (θ) - 3 cos (θ) = 2

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