What is the value of ln(sec(pi/3)+tan(pi/3)) ?

The value of ln(sec(pi/3)+tan(pi/3)) is ln(2+sqrt(3))

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ln(sec(pi/3)+tan(pi/3))

ln (sec (\frac{π}{3}) + tan (\frac{π}{3}))

ln (2 + 3)

Decimal Notation

1.31695 \dots

Solution steps

ln (sec (\frac{π}{3}) + tan (\frac{π}{3}))

Use the following trivial identity:

sec (\frac{π}{3}) = 2

sec (\frac{π}{3})

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}{3}) = 3

tan (\frac{π}{3})

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}

= 3

= ln (2 + 3)

cos (12 0^{\circ}) + tan^{2} (24 0^{\circ}) - 5

\frac{cos ( 6 0 ^{\circ} )}{cos ( 4 5 ^{\circ} )}

arctan (tan (\frac{5 π}{7}))

sin^{3} (1)

sin (\frac{π ^{2}}{9})

What is the value of ln(sec(pi/3)+tan(pi/3)) ?
The value of ln(sec(pi/3)+tan(pi/3)) is ln(2+sqrt(3))