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

The value of csc^2(30)-cot^2(45) is 3

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csc^2(30)-cot^2(45)

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

3

Solution steps

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

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:

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

= 2^{2} - 1^{2}

Simplify

= 3

ln (sec (1))

1 sin (1) - 1

1 arctan (1)

cot (4 3^{\circ})

6 1^{2} + 6 3^{2} - 2 \cdot 61 \cdot 63 \cdot cos (14 2^{\circ})

What is the value of csc^2(30)-cot^2(45) ?
The value of csc^2(30)-cot^2(45) is 3