What is the value of sec^2(-pi/3)-1 ?

The value of sec^2(-pi/3)-1 is 3

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sec^2(-pi/3)-1

sec^{2} (- \frac{π}{3}) - 1

3

Solution steps

sec^{2} (- \frac{π}{3}) - 1

Rewrite using trig identities:

sec (- \frac{π}{3}) = 2

sec (- \frac{π}{3})

Use the following property:

sec (- x) = sec (x)

sec (- \frac{π}{3}) = sec (\frac{π}{3})

= sec (\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^{2} - 1

Simplify

= 3

sec (arctan (\frac{3}{4}))

csc (- \frac{19 π}{6})

5 sin (\frac{3 π}{4})

- csc (\frac{π}{6})

tan (\frac{5 π}{6} + \frac{π}{4})