What is the value of 4sec^2(pi/4) ?

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4sec^2(pi/4)

4 sec^{2} (\frac{π}{4})

8

Solution steps

4 sec^{2} (\frac{π}{4})

Use the following trivial identity:

sec (\frac{π}{4}) = 2

sec (\frac{π}{4})

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 2

= 4 (2)^{2}

Simplify

4 (2)^{2} : 8

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

= 4 \cdot 2

Multiply the numbers:

4 \cdot 2 = 8

= 8

= 8

4 sec^{2} (\frac{π}{3})

cot (7 6^{\circ})

e^{0} cos (2)

(2 (cos (\frac{π}{3}) + i sin (\frac{π}{3})))^{3}

cos (- 6 0^{\circ}) \cdot sin (- 24 0^{\circ})