What is the value of tan(45)+sec(60) ?

The value of tan(45)+sec(60) is 3

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tan(45)+sec(60)

tan (4 5^{\circ}) + sec (6 0^{\circ})

3

Solution steps

tan (4 5^{\circ}) + sec (6 0^{\circ})

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

Use the following trivial identity:

sec (6 0^{\circ}) = 2

sec (6 0^{\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

= 1 + 2

Simplify

= 3

arccsc (sin (- \frac{π}{2}))

\frac{50 sin ( 4 1 ^{\circ} )}{100}

ln 4 + tan (\frac{π}{4})

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

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