What is the value of -2csc^2(pi/4)cot(pi/4) ?

The value of -2csc^2(pi/4)cot(pi/4) is -4

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-2csc^2(pi/4)cot(pi/4)

- 2 csc^{2} (\frac{π}{4}) cot (\frac{π}{4})

- 4

Solution steps

- 2 csc^{2} (\frac{π}{4}) cot (\frac{π}{4})

Use the following trivial identity:

csc (\frac{π}{4}) = 2

csc (\frac{π}{4})

csc (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= 2

Use the following trivial identity:

cot (\frac{π}{4}) = 1

cot (\frac{π}{4})

cot (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= 1

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

Simplify

- 2 (2)^{2} \cdot 1 : - 4

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

(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

= - 2 \cdot 2 \cdot 1

Multiply the numbers:

2 \cdot 2 \cdot 1 = 4

= - 4

= - 4

\frac{2 sin ( 3 0 ^{\circ} )}{cos ( 3 0 ^{\circ} )}

tan (\frac{2}{6})

sin (31. 7^{\circ})

cos (\frac{11 π}{20}) cos (\frac{π}{5}) - sin (\frac{11 π}{20}) sin (\frac{π}{5})

\frac{tan ( 5 0 ^{\circ} ) + tan ( 2 0 ^{\circ} )}{1 - tan ( 5 0 ^{\circ} ) tan ( 2 0 ^{\circ} )}

What is the value of -2csc^2(pi/4)cot(pi/4) ?
The value of -2csc^2(pi/4)cot(pi/4) is -4