What is the value of sec(-pi/(12)) ?

The value of sec(-pi/(12)) is sqrt(6)-sqrt(2)

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sec(-pi/(12))

sec (- \frac{π}{12})

6 - 2

Solution steps

sec (- \frac{π}{12})

Use the following property:

sec (- x) = sec (x)

sec (- \frac{π}{12}) = sec (\frac{π}{12})

= sec (\frac{π}{12})

Rewrite using trig identities:

\frac{1}{cos ( \frac{π}{12} )}

= \frac{1}{cos ( \frac{π}{12} )}

Rewrite using trig identities:

cos (\frac{π}{12}) = \frac{6 + 2}{4}

= \frac{1}{\frac{6 + 2}{4}}

Simplify

\frac{1}{\frac{6 + 2}{4}} : 6 - 2

= 6 - 2

cos (\frac{3}{2})

sin (arcsin (\frac{3}{2}))

cos (- \frac{2}{2})

5 cos (7 0^{\circ})

cos (\frac{3 π}{7}) cos (\frac{2 π}{21}) + sin (\frac{3 π}{7}) sin (\frac{2 π}{21})

What is the value of sec(-pi/(12)) ?
The value of sec(-pi/(12)) is sqrt(6)-sqrt(2)