What is the general solution for tan(θ)(sec(θ)-1)=0 ?

The general solution for tan(θ)(sec(θ)-1)=0 is θ=pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(θ)(sec(θ)-1)=0

tan (θ) (sec (θ) - 1) = 0

θ = πn

Degrees

θ = 0^{\circ} + 18 0^{\circ} n

Solution steps

tan (θ) (sec (θ) - 1) = 0

Solving each part separately

tan (θ) = 0 or sec (θ) - 1 = 0

tan (θ) = 0 : θ = πn

tan (θ) = 0

General solutions for

tan (θ) = 0

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

θ = 0 + πn

θ = 0 + πn

Solve

θ = 0 + πn : θ = πn

θ = 0 + πn

0 + πn = πn

θ = πn

θ = πn

sec (θ) - 1 = 0 : θ = 2 πn

sec (θ) - 1 = 0

Move

1

to the right side

sec (θ) - 1 = 0

Add

1

to both sides

sec (θ) - 1 + 1 = 0 + 1

Simplify

sec (θ) = 1

sec (θ) = 1

General solutions for

sec (θ) = 1

sec (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

θ = 0 + 2 πn

θ = 0 + 2 πn

Solve

θ = 0 + 2 πn : θ = 2 πn

θ = 0 + 2 πn

0 + 2 πn = 2 πn

θ = 2 πn

θ = 2 πn

Combine all the solutions

θ = πn, θ = 2 πn

Merge Overlapping Intervals

θ = πn

tan (x) + sec (x) = 2

sin (x) = \frac{4}{5}, \frac{π}{2} \leq x \leq π

2 - 2 cosh (t - 2) = 0

cos (x) = \frac{1}{37}

\frac{sin ( 2 x )}{cos ( x )} = 4 + sin (2 x) \cdot tan (x)

What is the general solution for tan(θ)(sec(θ)-1)=0 ?
The general solution for tan(θ)(sec(θ)-1)=0 is θ=pin