What is the general solution for -2sin(x)+5sin^2(x)=0 ?

The general solution for -2sin(x)+5sin^2(x)=0 is x=0.41151…+2pin,x=pi-0.41151…+2pin,x=2pin,x=pi+2pin

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-2sin(x)+5sin^2(x)=0

- 2 sin (x) + 5 sin^{2} (x) = 0

x = 0.41151 \dots + 2 πn, x = π - 0.41151 \dots + 2 πn, x = 2 πn, x = π + 2 πn

Solution steps

- 2 sin (x) + 5 sin^{2} (x) = 0

Solve by substitution

sin (x) = \frac{2}{5}, sin (x) = 0

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

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

Show solutions in decimal form

x = 0.41151 \dots + 2 πn, x = π - 0.41151 \dots + 2 πn, x = 2 πn, x = π + 2 πn

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

cos^{4} (x) = \frac{sin ^{2} ( x ) - 1}{4}

2 \cdot sin (x) + 1 = 0

5 cos^{2} (2 x) + 4 cos^{2} (x) - 5 = 0

sin (3 x + 10) = cos (x + 2 4^{\circ})

What is the general solution for -2sin(x)+5sin^2(x)=0 ?
The general solution for -2sin(x)+5sin^2(x)=0 is x=0.41151…+2pin,x=pi-0.41151…+2pin,x=2pin,x=pi+2pin