What is the value of 2sec^2(pi/3)tan(pi/3) ?

The value of 2sec^2(pi/3)tan(pi/3) is 8sqrt(3)

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2sec^2(pi/3)tan(pi/3)

2 sec^{2} (\frac{π}{3}) tan (\frac{π}{3})

83

Decimal Notation

13.85640 \dots

Solution steps

2 sec^{2} (\frac{π}{3}) tan (\frac{π}{3})

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

Use the following trivial identity:

tan (\frac{π}{3}) = 3

tan (\frac{π}{3})

tan (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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 3

= 2 \cdot 2^{2} 3

Simplify

2 \cdot 2^{2} 3 : 83

2 \cdot 2^{2} 3

Apply exponent rule:

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

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

= 2^{1 + 2} 3

Add the numbers:

1 + 2 = 3

= 2^{3} 3

2^{3} = 8

= 83

= 83

sin (11 π)

arcsin (\frac{11 sin ( 7 3 ^{\circ} )}{12})

- 2 sin (\frac{3 π}{4})

arctan (0.7)

cos (\frac{π}{4}) + i sin (\frac{π}{4})

What is the value of 2sec^2(pi/3)tan(pi/3) ?
The value of 2sec^2(pi/3)tan(pi/3) is 8sqrt(3)