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

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

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

- csc (\frac{π}{4}) cot (\frac{π}{4})

- 2

Decimal Notation

- 1.41421 \dots

Solution steps

- csc (\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 \cdot 1

Simplify

= - 2

tan (\frac{1}{2} arccos (\frac{2}{3}))

sin (π \cdot 0)

1 cos (6 0^{\circ})

sin (2 arccos (\frac{1}{3}))

arccos (\frac{43}{87})

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