What is the general solution for 1/(cos(x))-(sin(x))/(cos(x))=cos(x) ?

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

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1/(cos(x))-(sin(x))/(cos(x))=cos(x)

\frac{1}{cos ( x )} - \frac{sin ( x )}{cos ( x )} = cos (x)

x = 2 πn, x = π + 2 πn

Solution steps

\frac{1}{cos ( x )} - \frac{sin ( x )}{cos ( x )} = cos (x)

Subtract

cos (x)

from both sides

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

Simplify

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

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

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = 1, sin (x) = 0

sin (x) = 1 : x = \frac{π}{2} + 2 πn

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

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

Since the equation is undefined for:

\frac{π}{2} + 2 πn

x = 2 πn, x = π + 2 πn

cos (x) = \frac{- 8}{9}

cos (x) = \frac{6}{7 76}

2 sin (φ) - 1 = 0

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

x, z = sin^{2} (x - 2 π y)

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