Question

If cos (A) = 1/2 with A in QIV, find sec (A/2).

Answer 1

`cos(A)= (1)/(2) \Rightarrow A=\pm (\pi)/(3) +2k\pi,k \in Z`

A ∈ IV quadrant ⇒
`A=- (\pi)/(3)`


`\sec{ (A)/(2)}= \frac{1}{\cos{(A)/(2)}}= \frac{1}{\cos{(- (\pi)/(3) )/(2)}}= \frac{1}{\cos{(- (\pi)/(6) )}}= \frac{1}{\cos{ (\pi)/(6)}}= (1)/( ( √(3) )/(2) ) = (2)/( √(3) )`