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)

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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)

\frac{5.5}{cos ( 6 1 ^{\circ} )}

arctan (\frac{6}{- 2})

arcsin (- \frac{3}{8})

cos (\frac{5 π}{12}) + cos (\frac{π}{12})

tan (0.3)

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)