What is the value of sec^2(2(pi/6))*2 ?

The value of sec^2(2(pi/6))*2 is 8

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sec^2(2(pi/6))*2

sec^{2} (2 (\frac{π}{6})) \cdot 2

8

Solution steps

sec^{2} (2 (\frac{π}{6})) \cdot 2

= sec^{2} (2 \cdot \frac{π}{6}) \cdot 2

Simplify:

2 \cdot \frac{π}{6} = \frac{π}{3}

2 \cdot \frac{π}{6}

Multiply fractions:

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

= \frac{π 2}{6}

Cancel the common factor:

2

= \frac{π}{3}

= sec^{2} (\frac{π}{3}) \cdot 2

Use the following trivial identity:

sec (\frac{π}{3}) = 2

sec (\frac{π}{3})

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

= 2^{2} \cdot 2

Simplify

2^{2} \cdot 2 : 8

2^{2} \cdot 2

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

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

= 2^{2 + 1}

Add the numbers:

2 + 1 = 3

= 2^{3}

2^{3} = 8

= 8

= 8

cos (\frac{7 π}{10})

\frac{39}{sin ( 3 2 ^{\circ} )}

8 cos (9 0^{\circ})

tan (\frac{24}{7})

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