What is the general solution for tan(θ)+sec(θ)=1 ?

The general solution for tan(θ)+sec(θ)=1 is θ=2pin+2pi

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tan(θ)+sec(θ)=1

tan (θ) + sec (θ) = 1

θ = 2 πn + 2 π

Solution steps

tan (θ) + sec (θ) = 1

Subtract

1

from both sides

tan (θ) + sec (θ) - 1 = 0

Express with sin, cos

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

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

1 - cos (θ) + sin (θ) = 0

Rewrite using trig identities

1 + 2 sin (θ - \frac{π}{4}) = 0

Move

1

to the right side

2 sin (θ - \frac{π}{4}) = - 1

Divide both sides by

2

sin (θ - \frac{π}{4}) = - \frac{2}{2}

General solutions for

sin (θ - \frac{π}{4}) = - \frac{2}{2}

θ - \frac{π}{4} = \frac{5 π}{4} + 2 πn, θ - \frac{π}{4} = \frac{7 π}{4} + 2 πn

Solve

θ - \frac{π}{4} = \frac{5 π}{4} + 2 πn : θ = 2 πn + \frac{3 π}{2}

Solve

θ - \frac{π}{4} = \frac{7 π}{4} + 2 πn : θ = 2 πn + 2 π

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

Since the equation is undefined for:

2 πn + \frac{3 π}{2}

θ = 2 πn + 2 π

6 sin (x) + 8 = 0

2 cos (x) - 7 = 4 sec (x)

3 (cos (2 x) + \frac{3}{2}) = 6

sin^{2} (x) - 3 = 2 sin (x)

tan^{2} (x) - (3 + 1) tan (x) + 3 = 0

What is the general solution for tan(θ)+sec(θ)=1 ?
The general solution for tan(θ)+sec(θ)=1 is θ=2pin+2pi