What is the value of cot^2(45)+csc(30)-sec^2(60) ?

The value of cot^2(45)+csc(30)-sec^2(60) is -1

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cot^2(45)+csc(30)-sec^2(60)

cot^{2} (4 5^{\circ}) + csc (3 0^{\circ}) - sec^{2} (6 0^{\circ})

- 1

Solution steps

cot^{2} (4 5^{\circ}) + csc (3 0^{\circ}) - sec^{2} (6 0^{\circ})

Use the following trivial identity:

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

cot (4 5^{\circ})

cot (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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= 1

Use the following trivial identity:

csc (3 0^{\circ}) = 2

csc (3 0^{\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

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} + 2 - 2^{2}

Simplify

= - 1

10 cos (7 5^{\circ})

\frac{62}{tan ( 4 8 ^{\circ} )}

\frac{1}{sin ( 5 5 ^{\circ} )}

arccos (0.456)

- 5 \cdot 2.09 \cdot sin (2.09 \cdot 1.5 - \frac{π}{2})

What is the value of cot^2(45)+csc(30)-sec^2(60) ?
The value of cot^2(45)+csc(30)-sec^2(60) is -1