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

Simplify

ln 3 + 2 : ln (3 + 2)

ln 3 + 2

Simplify

3 + 2 : 3 + 2

3 + 2

Apply absolute rule:

∣ A ∣ = A, A \geq 0

3 + 2 = 3 + 2

= 3 + 2

= ln (3 + 2)

= ln (3 + 2)

2 sin (\frac{3 π}{5}) cos (\frac{3 π}{5})

sin (7.6)

3 \cdot sin (\frac{π}{4})

2 sin (\frac{2 π}{11}) cos (\frac{2 π}{11})

arctan (\frac{3.73}{9.8} + 0.6)

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)