What is the value of sec(45)+2tan(45) ?

The value of sec(45)+2tan(45) is sqrt(2)+2

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sec(45)+2tan(45)

sec (4 5^{\circ}) + 2 tan (4 5^{\circ})

2 + 2

Decimal Notation

3.41421 \dots

Solution steps

sec (4 5^{\circ}) + 2 tan (4 5^{\circ})

Use the following trivial identity:

sec (4 5^{\circ}) = 2

sec (4 5^{\circ})

sec (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 2

Use the following trivial identity:

tan (4 5^{\circ}) = 1

tan (4 5^{\circ})

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

= 2 + 2 \cdot 1

Simplify

= 2 + 2

csc (1 8^{\circ})

cos (58 5^{\circ})

sin (arcsin (\frac{2}{3}) + arccos (\frac{1}{3}))

- cos (\frac{5 π}{4})

cos (\frac{8 π}{5})

What is the value of sec(45)+2tan(45) ?
The value of sec(45)+2tan(45) is sqrt(2)+2