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

The value of sec(pi/4)tan(pi/4) is square root of 2

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

sec (\frac{π}{4}) tan (\frac{π}{4})

2

Decimal Notation

1.41421 \dots

Solution steps

sec (\frac{π}{4}) tan (\frac{π}{4})

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

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

= 2 \cdot 1

Simplify

= 2

arctan (tan (\frac{4 π}{3}))

sec (- \frac{7 π}{6})

tan (arcsin (\frac{5}{13}))

arccos (cos (\frac{3 π}{2}))

sec (\frac{10 π}{3})

What is the value of sec(pi/4)tan(pi/4) ?
The value of sec(pi/4)tan(pi/4) is square root of 2