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

The value of cot^2(45)-csc^2(45) is -1

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

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

- 1

Solution steps

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

= 1^{2} - (2)^{2}

Simplify

1^{2} - (2)^{2} : - 1

1^{2} - (2)^{2}

Apply rule

1^{a} = 1

1^{2} = 1

= 1 - (2)^{2}

(2)^{2} = 2

(2)^{2}

Apply radical rule:

a = a^{\frac{1}{2}}

= (2^{\frac{1}{2}})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 2^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

= 2

= 1 - 2

Subtract the numbers:

1 - 2 = - 1

= - 1

= - 1

arcsin (1.2)

1 + sin (0)

\frac{1}{tan ( \frac{π}{2} )}

cos (\frac{- 5 π}{12})

cos (99 0^{\circ})

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