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

The value of tan(pi/4)+sec(pi/4) is 1+sqrt(2)

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tan(pi/4)+sec(pi/4)

tan (\frac{π}{4}) + sec (\frac{π}{4})

1 + 2

Decimal Notation

2.41421 \dots

Solution steps

tan (\frac{π}{4}) + sec (\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

Use the following trivial identity:

sec (\frac{π}{4}) = 2

sec (\frac{π}{4})

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

= 1 + 2

sec (- 31 5^{\circ})

4 cos (12 0^{\circ})

tan (arcsin (\frac{9}{10}))

arccos (\frac{4}{6})

cos (2 arctan (- \frac{4}{3}))

What is the value of tan(pi/4)+sec(pi/4) ?
The value of tan(pi/4)+sec(pi/4) is 1+sqrt(2)