What is the general solution for 2-sqrt(-1-6sin(x))=sqrt(-4sin(x)) ?

The general solution for 2-sqrt(-1-6sin(x))=sqrt(-4sin(x)) is x=-0.30674…+2pin,x=pi+0.30674…+2pin

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2-sqrt(-1-6sin(x))=sqrt(-4sin(x))

2 - - 1 - 6 sin (x) = - 4 sin (x)

x = - 0.30674 \dots + 2 πn, x = π + 0.30674 \dots + 2 πn

Solution steps

2 - - 1 - 6 sin (x) = - 4 sin (x)

Solve by substitution

sin (x) = \frac{- 21 + 4 26}{2}

sin (x) = \frac{- 21 + 4 26}{2} : x = arcsin (\frac{- 21 + 4 26}{2}) + 2 πn, x = π + arcsin (- \frac{- 21 + 4 26}{2}) + 2 πn

Combine all the solutions

x = arcsin (\frac{- 21 + 4 26}{2}) + 2 πn, x = π + arcsin (- \frac{- 21 + 4 26}{2}) + 2 πn

Show solutions in decimal form

x = - 0.30674 \dots + 2 πn, x = π + 0.30674 \dots + 2 πn

2 sin (\frac{x}{2}) - 1 = 0

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

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

tan^{2} (x) + 3 = 0

4 cos (θ) + 1 = 0

What is the general solution for 2-sqrt(-1-6sin(x))=sqrt(-4sin(x)) ?
The general solution for 2-sqrt(-1-6sin(x))=sqrt(-4sin(x)) is x=-0.30674…+2pin,x=pi+0.30674…+2pin