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

The value of csc(pi/2)-cot(pi/2) is 1

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

csc (\frac{π}{2}) - cot (\frac{π}{2})

1

Solution steps

csc (\frac{π}{2}) - cot (\frac{π}{2})

Use the following trivial identity:

csc (\frac{π}{2}) = 1

csc (\frac{π}{2})

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

= 1

Use the following trivial identity:

cot (\frac{π}{2}) = 0

cot (\frac{π}{2})

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

= 0

= 1 - 0

Simplify

= 1

arctan (\frac{- 5}{0})

sin (1.5 π)

cos (\frac{2}{3})

sin (\frac{12}{20})

\frac{5.3}{cos ( 5 1 ^{\circ} )}

What is the value of csc(pi/2)-cot(pi/2) ?
The value of csc(pi/2)-cot(pi/2) is 1