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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sec(θ)+tan(θ)=1

sec (θ) + tan (θ) = 1

θ = 2 πn + 2 π

Solution steps

sec (θ) + tan (θ) = 1

Subtract

1

from both sides

sec (θ) + tan (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

x, 2 cos^{2} (x) = 1

sin (2 θ - \frac{π}{3}) = - \frac{1}{2}

sec (x) + cos (x) = sin (x) tan (x)

7 cos (θ) + 20 = 0

sec^{2} (x) = \frac{1}{2} csc^{2} (x) + tan^{2} (x)

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