What is the general solution for (1+sin(x))(1+sin(x))=cos^2(x) ?

The general solution for (1+sin(x))(1+sin(x))=cos^2(x) is x=2pin+pi,x=2pin+(3pi)/2 ,x=2pin+2pi

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(1+sin(x))(1+sin(x))=cos^2(x)

(1 + sin (x)) (1 + sin (x)) = cos^{2} (x)

x = 2 πn + π, x = 2 πn + \frac{3 π}{2}, x = 2 πn + 2 π

Solution steps

(1 + sin (x)) (1 + sin (x)) = cos^{2} (x)

Subtract

cos^{2} (x)

from both sides

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

Factor

(1 + sin (x))^{2} - cos^{2} (x) : (1 + sin (x) + cos (x)) (1 + sin (x) - cos (x))

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

Solving each part separately

1 + sin (x) + cos (x) = 0 or 1 + sin (x) - cos (x) = 0

1 + sin (x) + cos (x) = 0 : x = 2 πn + π, x = 2 πn + \frac{3 π}{2}

1 + sin (x) - cos (x) = 0 : x = 2 πn + \frac{3 π}{2}, x = 2 πn + 2 π

Combine all the solutions

x = 2 πn + π, x = 2 πn + \frac{3 π}{2}, x = 2 πn + 2 π

cos (θ) = - 0.866

cos (θ) = \frac{2 5}{19}

3 csc (θ) + csc (θ) cot (θ) = 0

tan (x) (cot (x) + 1) = 0

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

What is the general solution for (1+sin(x))(1+sin(x))=cos^2(x) ?
The general solution for (1+sin(x))(1+sin(x))=cos^2(x) is x=2pin+pi,x=2pin+(3pi)/2 ,x=2pin+2pi