What is the general solution for sin^2(x)-4sin(x)+1=0 ?

The general solution for sin^2(x)-4sin(x)+1=0 is x=0.27126…+2pin,x=pi-0.27126…+2pin

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sin^2(x)-4sin(x)+1=0

sin^{2} (x) - 4 sin (x) + 1 = 0

x = 0.27126 \dots + 2 πn, x = π - 0.27126 \dots + 2 πn

Solution steps

sin^{2} (x) - 4 sin (x) + 1 = 0

Solve by substitution

sin (x) = 2 + 3, sin (x) = 2 - 3

sin (x) = 2 + 3 :

No Solution

sin (x) = 2 - 3 : x = arcsin (2 - 3) + 2 πn, x = π - arcsin (2 - 3) + 2 πn

Combine all the solutions

x = arcsin (2 - 3) + 2 πn, x = π - arcsin (2 - 3) + 2 πn

Show solutions in decimal form

x = 0.27126 \dots + 2 πn, x = π - 0.27126 \dots + 2 πn

6 sin (2 x) + 2 sin (x) = 0

3 sin^{2} (w) - 4 sin (w) - 4 = 0

sin (θ) = \frac{9}{10}

2 sec^{2} (x) - tan^{2} (x) = 3

tan (x) - 2 sin (x) = 0

What is the general solution for sin^2(x)-4sin(x)+1=0 ?
The general solution for sin^2(x)-4sin(x)+1=0 is x=0.27126…+2pin,x=pi-0.27126…+2pin