What is the general solution for sin^2(x)=((7m-2))/8 ?

The general solution for sin^2(x)=((7m-2))/8 is

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sin^2(x)=((7m-2))/8

sin^{2} (x) = \frac{( 7 m - 2 )}{8}

x = arcsin (\frac{2 7 m - 2}{4}) + 2 πn, x = π + arcsin (- \frac{2 7 m - 2}{4}) + 2 πn, x = arcsin (- \frac{2 7 m - 2}{4}) + 2 πn, x = π + arcsin (\frac{2 7 m - 2}{4}) + 2 πn

Solution steps

sin^{2} (x) = \frac{( 7 m - 2 )}{8}

Solve by substitution

sin (x) = \frac{2 7 m - 2}{4}, sin (x) = - \frac{2 7 m - 2}{4}

sin (x) = \frac{2 7 m - 2}{4} : x = arcsin (\frac{2 7 m - 2}{4}) + 2 πn, x = π + arcsin (- \frac{2 7 m - 2}{4}) + 2 πn

sin (x) = - \frac{2 7 m - 2}{4} : x = arcsin (- \frac{2 7 m - 2}{4}) + 2 πn, x = π + arcsin (\frac{2 7 m - 2}{4}) + 2 πn

Combine all the solutions

x = arcsin (\frac{2 7 m - 2}{4}) + 2 πn, x = π + arcsin (- \frac{2 7 m - 2}{4}) + 2 πn, x = arcsin (- \frac{2 7 m - 2}{4}) + 2 πn, x = π + arcsin (\frac{2 7 m - 2}{4}) + 2 πn

cos (θ) + 2 = 0

2 sec (x) = 2 tan (x) + 3 sec (x)

4 cos (x) + 3 sin (x) = 5

sin (x) - csc (x) + 1 = 0

tan^{2} (θ) - sec^{2} (θ) = cos (- θ)

What is the general solution for sin^2(x)=((7m-2))/8 ?
The general solution for sin^2(x)=((7m-2))/8 is