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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

ln (1 + 2)

Decimal Notation

0.88137 \dots

Solution steps

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

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

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

= ln (1 + 2)

tan^{2} (5 4^{\circ})

sin (24 0^{\circ} - 31 5^{\circ})

2 sin (15 0^{\circ}) - 1

arctan (\frac{24}{- 7})

3 tan (5 3^{\circ})

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