What is the value of ln(2+tan(pi/4)) ?

The value of ln(2+tan(pi/4)) is ln(3)

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ln(2+tan(pi/4))

ln (2 + tan (\frac{π}{4}))

ln (3)

Decimal Notation

1.09861 \dots

Solution steps

ln (2 + tan (\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

= ln (2 + 1)

Simplify

= ln (3)

70 \cdot sin (5 0^{\circ})

arccosh (\frac{25}{7})

\frac{5}{tan ( 2 0 ^{\circ} )}

arctan (1.96)

- 10 cos (0)