What is the value of sec(45)csc(45)-1 ?

The value of sec(45)csc(45)-1 is 1

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sec(45)csc(45)-1

sec (4 5^{\circ}) csc (4 5^{\circ}) - 1

1

Solution steps

sec (4 5^{\circ}) csc (4 5^{\circ}) - 1

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:

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

csc (4 5^{\circ})

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= 2

= 22 - 1

Simplify

22 - 1 : 1

22 - 1

Apply radical rule:

a a = a

22 = 2

= 2 - 1

Subtract the numbers:

2 - 1 = 1

= 1

= 1

9 + cos (2) - cos (1)

arccos (sin (- \frac{2 π}{3}))

20 cos (\frac{2 π}{3})

\frac{250}{sin ( 4 5 ^{\circ} )}

arctan (\frac{11.2}{18.3})