Question

How do you find the exact functional value sec (-pi/12) using the cosine sum or difference identity?

Answer 1

`sec(-pi/12)=(2sqrt2)/(sqrt3 +1)`

Explanation:

`sec(-pi/12)= sec(pi/12)= sec15 = 1/cos 15`. This cannot be evaluated by using cosine sum or difference identity. Half angle identity is used instead to find cos 15.

cos 30 = `2cos^2 15 -1`

cos 15= `sqrt((1+cos30)/2)`=`sqrt(2+sqrt3)/2`=`(sqrt3 +1)/(2sqrt2)`

That gives `sec(-pi/12)=(2sqrt2)/(sqrt3 +1)`