Question

What is the value of sec 15 ?

Answer 1

$cos(2x) = 2 cos^{2}(x) - 1\\ \\ x = 15 \\ \\ cos(30) = 2 cos^{2}(15) - 1 \\ \\ cos(15) = \sqrt{ \frac{\frac{ \sqrt{3} }{2} + 1}{2} } \\ \\ cos(15) = \frac{ \sqrt{\sqrt{3} + 2} }{2} \\ \\ sec(15) = \frac{2}{ \sqrt{\sqrt{3} + 2}}$

Answer 2

sec 15 = 1/cos 15
so cos 15 = cos(45 - 30)= cos45cos30 + sin45sin30
                                     =(1/√2)(√3/2) + (1/√2)(1/2)
                                      = (√3 + 1)/(2√2) 
so 1/cos 15= (2√2) / (√3 + 1)
sec 15 =  (2√2) / (√3 + 1)