trig Identities 9

Mathematics
Tutor: None Selected Time limit: 1 Day

Find the exact value for sec(5pie/12)

Dec 17th, 2014

square route of 6 + square route of 2

Let's see, 5pi/12 = 3pi/12 + 2pi/12 = pi/4 + pi/6, so you can change the secant to a cosine and apply the cosine addition formula. 

sec(5pi/12) = 
1 / cos(5pi/12) = 
1 / cos(pi/4 + pi/6) = 
1 / [ cos(pi/4)cos(pi/6) - sin(pi/4)sin(pi/6) ] = 
1 / [ (√2 / 2)(√3 /2) - (√2 / 2)(1/2) ] 
4 / [ √2√3 - √2 ] 
4 / [ √6 - √2 ] 
4(√6+√2) / (√6-√2)(√6+√2) 
4(√6+√2) / (6 - 2) 
√6 + √2

Dec 17th, 2014

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