What is the general solution for (2-2sin(x))/a = 2/(sin(x)) ?

The general solution for (2-2sin(x))/a = 2/(sin(x)) is

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(2-2sin(x))/a = 2/(sin(x))

\frac{2 - 2 sin ( x )}{a} = \frac{2}{sin ( x )}

x = arcsin (- \frac{- 1 + - 4 a + 1}{2}) + 2 πn, x = π + arcsin (\frac{- 1 + - 4 a + 1}{2}) + 2 πn, x = arcsin (\frac{- 4 a + 1 + 1}{2}) + 2 πn, x = π + arcsin (- \frac{- 4 a + 1 + 1}{2}) + 2 πn

Solution steps

\frac{2 - 2 sin ( x )}{a} = \frac{2}{sin ( x )}

Solve by substitution

sin (x) = - \frac{- 1 + - 4 a + 1}{2}, sin (x) = \frac{- 4 a + 1 + 1}{2}; a \neq = 0

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

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

Combine all the solutions

x = arcsin (- \frac{- 1 + - 4 a + 1}{2}) + 2 πn, x = π + arcsin (\frac{- 1 + - 4 a + 1}{2}) + 2 πn, x = arcsin (\frac{- 4 a + 1 + 1}{2}) + 2 πn, x = π + arcsin (- \frac{- 4 a + 1 + 1}{2}) + 2 πn

sin (B) = \frac{1}{3}

cos (7 x) = sin (5 x - 6)

100 = 211.49 - 20.96 cosh (0.03291765 x)

3 sec^{2} (x) + 4 cos^{2} (x) = 7

cos (θ) = \frac{43}{90}

What is the general solution for (2-2sin(x))/a = 2/(sin(x)) ?
The general solution for (2-2sin(x))/a = 2/(sin(x)) is