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

The value of -sec(pi/3)+2sec^3(pi/3) is 14

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-sec(pi/3)+2sec^3(pi/3)

- sec (\frac{π}{3}) + 2 sec^{3} (\frac{π}{3})

14

Solution steps

- sec (\frac{π}{3}) + 2 sec^{3} (\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

= - 2 + 2 \cdot 2^{3}

Simplify

- 2 + 2 \cdot 2^{3} : 14

- 2 + 2 \cdot 2^{3}

2 \cdot 2^{3} = 2^{4}

2 \cdot 2^{3}

Apply exponent rule:

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

2 \cdot 2^{3} = 2^{1 + 3}

= 2^{1 + 3}

Add the numbers:

1 + 3 = 4

= 2^{4}

= - 2 + 2^{4}

2^{4} = 16

= - 2 + 16

Add/Subtract the numbers:

- 2 + 16 = 14

= 14

= 14

30 cos (12 0^{\circ})

sec (1 9^{\circ})

tan (\frac{7 π}{6} + \frac{3 π}{4})

cot (arccsc (\frac{π}{4}))

\frac{4}{tan ( 3 6 ^{\circ} )}

What is the value of -sec(pi/3)+2sec^3(pi/3) ?
The value of -sec(pi/3)+2sec^3(pi/3) is 14