SOLUTION: I need to solve this compound formula (exact solution): sec(π/3 - 5π/4) I have attempted to solve it but I end up with {{{ 2sqrt(2)/(sqrt(3) -2) }}}.

Algebra ->  Trigonometry-basics -> SOLUTION: I need to solve this compound formula (exact solution): sec(π/3 - 5π/4) I have attempted to solve it but I end up with {{{ 2sqrt(2)/(sqrt(3) -2) }}}.      Log On


   

Question 957479: I need to solve this compound formula (exact solution): sec(π/3 - 5π/4)
I have attempted to solve it but I end up with +2sqrt%282%29%2F%28sqrt%283%29+-2%29+.
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
I need to solve this compound formula (exact solution):
sec(π/3 - 5π/4)
-------
= 1/[cos(pi/3 - 5pi/4)
-------
= 1/[cos(pi/3)*cos(5pi/4) - sin(pi/3)sin(5pi/4)]
-------
= 1/[(1/2)*(-sqrt(2)/2) - (sqrt(3)/2)*(-sqrt(2)/2)]
--------
= 1/[-sqrt(2)/4 + sqrt(6)/4]
---------
= 4/[sqrt(6)-sqrt(2)]
----
= 4[sqrt(6)+sqrt(2)]/[6-2]
----
= sqrt(6)+sqrt(2)
-----------------------
Cheers,
Stan H.
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Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
The other tutor's solution is incorrect.

He has a sign wrong in the formula for cos%28alpha-beta%29=cos%28alpha%29cos%28beta%29%2Bsin%28alpha%29sin%28beta%29

sec%28pi%2F3+-+5pi%2F4%29%22%22=%22%22

1%2Fcos%28pi%2F3+-+5pi%2F4%29%22%22=%22%22

1%2F%28cos%28pi%2F3%29cos%285pi%2F4%29%2Bsin%28pi%2F3%29sin%285pi%2F4%29%29%22%22=%22%22

1%2F%28%281%2F2%29%28-sqrt%282%29%2F2%29%2B%28sqrt%283%29%2F2%29%28-sqrt%282%29%2F2%29%29%22%22=%22%22 

1%2F%28-sqrt%282%29%2F4-sqrt%286%29%2F4%29%22%22=%22%22 

1%2F%28%28-sqrt%282%29-sqrt%286%29%29%2F4%29%29%22%22=%22%22

1%2A%28expr%284%2F%28-sqrt%282%29-sqrt%286%29%29%29%29%29%22%22=%22%22

expr%284%2F%28-sqrt%282%29-sqrt%286%29%29%29%29%22%22=%22%22  

Rationalize the denominator:

%22%22=%22%22

+4%28+-sqrt%282%29%2Bsqrt%286%29+%29%2F%282-6%29

+4%28+-sqrt%282%29%2Bsqrt%286%29+%29%2F%28-4%29

+cross%284%29%28+-sqrt%282%29%2Bsqrt%286%29+%29%2F%28-cross%284%29%29

+%28+-sqrt%282%29%2Bsqrt%286%29+%29%2F%28-1%29

+-%28-sqrt%282%29%2Bsqrt%286%29+%29

+sqrt%282%29-sqrt%286%29

Edwin