What is the general solution for 8sin^2(x)-2sin(x)-1=0,-pi/2 <x< pi/2 ?

The general solution for 8sin^2(x)-2sin(x)-1=0,-pi/2 <x< pi/2 is x= pi/6 ,x=-0.25268…

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8sin^2(x)-2sin(x)-1=0,-pi/2 <x< pi/2

8 sin^{2} (x) - 2 sin (x) - 1 = 0, - \frac{π}{2} < x < \frac{π}{2}

x = \frac{π}{6}, x = - 0.25268 \dots

Solution steps

8 sin^{2} (x) - 2 sin (x) - 1 = 0, - \frac{π}{2} < x < \frac{π}{2}

Solve by substitution

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

sin (x) = \frac{1}{2}, - \frac{π}{2} < x < \frac{π}{2} : x = \frac{π}{6}

sin (x) = - \frac{1}{4}, - \frac{π}{2} < x < \frac{π}{2} : x = - arcsin (\frac{1}{4})

Combine all the solutions

x = \frac{π}{6}, x = - arcsin (\frac{1}{4})

Show solutions in decimal form

x = \frac{π}{6}, x = - 0.25268 \dots

cos (4 x) - cos (3 x) = 0

2 cos^{2} (A) + cos (A) - 1 = 0

tan^{3} (x) = tan (x), 0 \leq x \leq 2 π

sin (x^{2} + 3 x + 5) = 0

sin (θ) (2 sin (θ) + 1) = 0

What is the general solution for 8sin^2(x)-2sin(x)-1=0,-pi/2 <x< pi/2 ?
The general solution for 8sin^2(x)-2sin(x)-1=0,-pi/2 <x< pi/2 is x= pi/6 ,x=-0.25268…