Question 957479
<pre>
The other tutor's solution is incorrect.

He has a sign wrong in the formula for {{{cos(alpha-beta)=cos(alpha)cos(beta)+sin(alpha)sin(beta)}}}

{{{sec(pi/3 - 5pi/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)}}}{{{""=""}}} 

{{{1/((-sqrt(2)-sqrt(6))/4))}}}{{{""=""}}}

{{{1*(expr(4/(-sqrt(2)-sqrt(6)))))}}}{{{""=""}}}

{{{expr(4/(-sqrt(2)-sqrt(6))))}}}{{{""=""}}}  

Rationalize the denominator:

{{{( 4/( -sqrt(2)-sqrt(6) ))

(   (-sqrt(2)+sqrt(6))/(-sqrt(2)+sqrt(6))   )

}}}{{{""=""}}}

{{{ 4( -sqrt(2)+sqrt(6) )/(2-6)}}}

{{{ 4( -sqrt(2)+sqrt(6) )/(-4)}}}

{{{ cross(4)( -sqrt(2)+sqrt(6) )/(-cross(4))}}}

{{{ ( -sqrt(2)+sqrt(6) )/(-1)}}}

{{{ -(-sqrt(2)+sqrt(6) )}}}

{{{ sqrt(2)-sqrt(6)}}}

Edwin</pre>