What is the general solution for sec(x)-tan(x)=cos(x) ?

The general solution for sec(x)-tan(x)=cos(x) is x=2pin,x=pi+2pin

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sec(x)-tan(x)=cos(x)

sec (x) - tan (x) = cos (x)

x = 2 πn, x = π + 2 πn

Solution steps

sec (x) - tan (x) = cos (x)

Subtract

cos (x)

from both sides

sec (x) - tan (x) - cos (x) = 0

Express with sin, cos

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

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

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

- 2 sin (x) = - sin (x) cos (x)

\frac{0.9}{cos ( x )} + (0.7 \cdot sin (x)) = 1.1

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

sin (\frac{x}{2}) = 1

cos (θ) sin (θ) = sin (2 θ)

What is the general solution for sec(x)-tan(x)=cos(x) ?
The general solution for sec(x)-tan(x)=cos(x) is x=2pin,x=pi+2pin