Question

How do you use the sum or difference identities to find the exact value of `sec795^circ`?

Answer 1

`sqrt 6 + sqrt 2`

Explanation:

Divide by 360. `1/{cos 795º} = 1/{cos 75º} = 1/{cos (45 + 30)º}`

`= 1/{cos a cos b - sin a sin b} = 1/{sqrt2/2 * sqrt 3/2 - sqrt 2/2 * 1/2}`

`= 4/{sqrt 2 (sqrt 3 - 1)} * frac{sqrt 2}{sqrt 2} * frac{sqrt 3 + 1}{sqrt 3 + 1}`

`= 2 sqrt 2 * (sqrt 3 + 1)/{3-1}`