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

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

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

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

- 1

Solution steps

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

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

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

= 2 \cdot 0 \cdot 1 - 1^{2}

Simplify

= - 1

arccos (\frac{37}{40})

cos (arcsin (\frac{5}{13}) - arctan (\frac{3}{4}))

4 sin (22 5^{\circ})

cos (\frac{7 π}{4} - \frac{5 π}{6})

\frac{4}{cos ( 2 1 ^{\circ} )}

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