What is the general solution for 25sin^2(x)-10sin(x)+1=0 ?

The general solution for 25sin^2(x)-10sin(x)+1=0 is x=0.20135…+2pin,x=pi-0.20135…+2pin

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25sin^2(x)-10sin(x)+1=0

25 sin^{2} (x) - 10 sin (x) + 1 = 0

x = 0.20135 \dots + 2 πn, x = π - 0.20135 \dots + 2 πn

Solution steps

25 sin^{2} (x) - 10 sin (x) + 1 = 0

Solve by substitution

sin (x) = \frac{1}{5}

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

Combine all the solutions

x = arcsin (\frac{1}{5}) + 2 πn, x = π - arcsin (\frac{1}{5}) + 2 πn

Show solutions in decimal form

x = 0.20135 \dots + 2 πn, x = π - 0.20135 \dots + 2 πn

4 - 4 sin (θ) = 2

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

cos (x) = \frac{84}{98}

cos (\frac{3 θ}{2}) = \frac{1}{2}

0 = 5 + 4 cos (x)

What is the general solution for 25sin^2(x)-10sin(x)+1=0 ?
The general solution for 25sin^2(x)-10sin(x)+1=0 is x=0.20135…+2pin,x=pi-0.20135…+2pin