SOLUTION: Use appropriate identities to find the exact values of the following. a. sec(75degrees) so far I have sec(45deg+30deg)? then stuck. b. sin(7pi/12) I think this co

Question 100848: Use appropriate identities to find the exact values of the following.
a. sec(75degrees)
so far I have sec(45deg+30deg)? then stuck.
b. sin(7pi/12)
I think this converts down to sin(2pi/3)? then stuck.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Use appropriate identities to find the exact values of the following.
a. sec(75degrees)
so far I have sec(45deg+30deg)? then stuck.
= 1/[cos(45+30)]
= 1/[cos45*cos30-sin45sin30]
= 1/[1/sqrt2 * sqrt3/2 - 1/sqrt2 *1/2]
= 1/[sqrt3/2sqrt2 - 1/2sqrt2]
= 2sqrt2/[sqrt3 - 1]
= [2sqrt2(sqrt3+1)]/[3-1]
= [2sqrt6 +2sqrt2]/2
= sqrt6 + sqrt2
=========================
b. sin(7pi/12)= sin(pi/3 + pi/4)
= sin(pi/3)cos(pi/4)+cos(pi/3)sin(pi/4)
= (sqrt3)/2 * (sqrt2)/2 + (1/2)(sqrt2)/2
= (sqrt6)/4 + (sqrt2)/4
= [sqrt6 + sqrt2]/4
===========================
Cheers,
Stan H.

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