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

1 Answer

Vinícius Ferraz

Dec 28, 2016

#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}#

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