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

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

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

- cot (\frac{π}{4}) csc (\frac{π}{4})

- 2

Decimal Notation

- 1.41421 \dots

Solution steps

- cot (\frac{π}{4}) csc (\frac{π}{4})

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

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

= - 1 \cdot 2

Simplify

= - 2

\frac{1}{2} arctan (\frac{2}{2})

sin (- \frac{3}{4} π)

\frac{sin ( 1 5 ^{\circ} ) - cos ( 1 5 ^{\circ} )}{tan ( 1 5 ^{\circ} )}

10 cos (3 7^{\circ})

arcsin (\frac{3.9}{8.1})

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