What is the value of sec^2(45)(pi/(180))*1 ?

The value of sec^2(45)(pi/(180))*1 is pi/(90)

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sec^2(45)(pi/(180))*1

sec^{2} (4 5^{\circ}) (\frac{π}{180}) \cdot 1

\frac{π}{90}

Decimal Notation

0.03490 \dots

Solution steps

sec^{2} (4 5^{\circ}) (1^{\circ}) \cdot 1

= sec^{2} (4 5^{\circ}) 1^{\circ} \cdot 1

Use the following trivial identity:

sec (4 5^{\circ}) = 2

sec (4 5^{\circ})

sec (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 2

= (2)^{2} 1^{\circ} \cdot 1

Simplify

(2)^{2} 1^{\circ} \cdot 1 : 2^{\circ}

(2)^{2} 1^{\circ} \cdot 1

(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 1 \cdot 1^{\circ}

Multiply fractions:

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

= 1 \cdot 2^{\circ}

Cancel the common factor:

2

= 1 \cdot 2^{\circ}

Multiply:

1 \cdot 2^{\circ} = 2^{\circ}

= 2^{\circ}

= 2^{\circ}

\frac{9 sin ( 3 1 ^{\circ} )}{tan ( 5 5 ^{\circ} )}

arctan (\frac{85}{50})

cos (74.4 9^{\circ})

\frac{1}{2} sin (3 (\frac{5 π}{6}) - π)

cos (74. 5^{\circ})

What is the value of sec^2(45)(pi/(180))*1 ?
The value of sec^2(45)(pi/(180))*1 is pi/(90)