What is the value of ln|sec(pi/4)+tan(pi/4)| ?

The value of ln|sec(pi/4)+tan(pi/4)| is ln(sqrt(2)+1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

ln|sec(pi/4)+tan(pi/4)|

ln sec (\frac{π}{4}) + tan (\frac{π}{4})

ln (2 + 1)

Decimal Notation

0.88137 \dots

Solution steps

ln sec (\frac{π}{4}) + tan (\frac{π}{4})

Use the following trivial identity:

sec (\frac{π}{4}) = 2

sec (\frac{π}{4})

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}

= 2

Use the following trivial identity:

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

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}

= 1

= ln 2 + 1

Simplify

ln 2 + 1 : ln (2 + 1)

ln 2 + 1

Simplify

2 + 1 : 2 + 1

2 + 1

Apply absolute rule:

∣ A ∣ = A, A \geq 0

2 + 1 = 2 + 1

= 2 + 1

= ln (2 + 1)

= ln (2 + 1)

7 cos (5.8 \cdot 180)

\frac{8 3}{3} sin (3 0^{\circ})

arccos (0.607)

8 cos (1 5^{\circ})

cos (36.6 9^{\circ})

What is the value of ln|sec(pi/4)+tan(pi/4)| ?
The value of ln|sec(pi/4)+tan(pi/4)| is ln(sqrt(2)+1)