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

The value of cot(pi/4)-pi/4 csc^2(pi/4) is 1-pi/2

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

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

1 - \frac{π}{2}

Decimal Notation

- 0.57079 \dots

Solution steps

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

Simplify

1 - \frac{π}{4} (2)^{2} : 1 - \frac{π}{2}

1 - \frac{π}{4} (2)^{2}

\frac{π}{4} (2)^{2} = \frac{π}{2}

\frac{π}{4} (2)^{2}

(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 \frac{π}{4}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{π 2}{4}

Cancel the common factor:

2

= \frac{π}{2}

= 1 - \frac{π}{2}

= 1 - \frac{π}{2}

- 6 cos (4 5^{\circ})

\frac{5}{cos ( 6 5 ^{\circ} )}

tan (1.33)

11 cos (4 5^{\circ})

16 sin (4 2^{\circ})

What is the value of cot(pi/4)-pi/4 csc^2(pi/4) ?
The value of cot(pi/4)-pi/4 csc^2(pi/4) is 1-pi/2