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

The value of ln|4+tan(pi/4)| is ln(5)

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ln|4+tan(pi/4)|

ln 4 + tan (\frac{π}{4})

ln (5)

Decimal Notation

1.60943 \dots

Solution steps

ln 4 + 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 ∣ 4 + 1 ∣

Simplify

ln ∣ 4 + 1 ∣ : ln (5)

ln ∣ 4 + 1 ∣

Add the numbers:

4 + 1 = 5

= ln ∣ 5 ∣

Simplify

∣ 5 ∣ : 5

∣ 5 ∣

Apply absolute rule:

∣ a ∣ = a, a \geq 0

∣ 5 ∣ = 5

= 5

= ln (5)

= ln (5)

80 \cdot 21 \cdot cos (2 3^{\circ})

sin (arccos (- \frac{15}{17}))

cos^{2} (6 2^{\circ})

\frac{1}{2} \cdot 5.4 \cdot 16 \cdot sin (6 2^{\circ})

- \frac{1}{2} sec^{2} (\frac{π}{4})