What is the general solution for sin^2(x)=sin^2(x)sec(x) ?

The general solution for sin^2(x)=sin^2(x)sec(x) is x=2pin,x=pi+2pin

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sin^2(x)=sin^2(x)sec(x)

sin^{2} (x) = sin^{2} (x) sec (x)

x = 2 πn, x = π + 2 πn

Solution steps

sin^{2} (x) = sin^{2} (x) sec (x)

Subtract

sin^{2} (x) sec (x)

from both sides

sin^{2} (x) - sin^{2} (x) sec (x) = 0

Factor

sin^{2} (x) - sin^{2} (x) sec (x) : - sin^{2} (x) (sec (x) - 1)

- sin^{2} (x) (sec (x) - 1) = 0

Solving each part separately

sin^{2} (x) = 0 or sec (x) - 1 = 0

sin^{2} (x) = 0 : x = 2 πn, x = π + 2 πn

sec (x) - 1 = 0 : x = 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn

sin (x) - cos (x) = 2

sin (x) = \frac{4.2}{9.5}

cos (x) = \frac{4.6}{8.6}

5 tan (x) + 5 tan^{2} (x) = 0

t, x = r cos (t)

What is the general solution for sin^2(x)=sin^2(x)sec(x) ?
The general solution for sin^2(x)=sin^2(x)sec(x) is x=2pin,x=pi+2pin