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

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

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

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

ln (3 + 2)

Decimal Notation

1.31695 \dots

Solution steps

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

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

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

= ln (3 + 2)

arccos (0.8333)

sin (2 arctan (3))

\frac{1}{cos ^{2} ( 4 0 ^{\circ} )} - \frac{1}{cot ^{2} ( 4 0 ^{\circ} )}

\frac{9}{sin ( 3 0 ^{\circ} )}

370 \cdot \frac{1}{cos ( 2 0 ^{\circ} )} \cdot sin (2 0^{\circ})

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