SOLUTION: Solve for {{{ (sin(pi/3)cos(pi/4)-sin(pi/4)cos(pi/3))^2 }}}.

Algebra ->  Finance -> SOLUTION: Solve for {{{ (sin(pi/3)cos(pi/4)-sin(pi/4)cos(pi/3))^2 }}}.      Log On


   

Question 1155584: Solve for +%28sin%28pi%2F3%29cos%28pi%2F4%29-sin%28pi%2F4%29cos%28pi%2F3%29%29%5E2+.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
+%28sin%28pi%2F3%29cos%28pi%2F4%29-sin%28pi%2F4%29cos%28pi%2F3%29%29%5E2+
%28sqrt%283%29%2F2%2A%281%2Fsqrt%282%29%29+-%281%2Fsqrt%282%29%29+%2A%281%2F2%29%29%5E2+
%28sqrt%283%29%2F2sqrt%282%29+-1%2F2sqrt%282%29%29%5E2+
%28%28sqrt%283%29+-1%29%2F%282sqrt%282%29%29%29%5E2+
%28sqrt%283%29+-1%29%5E2%2F%282sqrt%282%29%29%5E2+
%283+-2sqrt%283%29%2B1%29%2F%284%2A2%29+
%284+-2sqrt%283%29%29%2F8+
1%2F2+-+sqrt%283%29%2F4+


or this way
use identity

%28sin%28pi%2F3-pi%2F4%29%29%5E2
%28sin%284pi%2F12-3pi%2F12%29%29%5E2
sin%5E2%28pi%2F12%29
1%2F2+-+sqrt%283%29%2F4

or, use the fact that angle pi%2F3=60° and %28pi%2F4%29=45°, then use unit circle
+%28sin%2860%29cos%2845%29-sin%2845%29cos%2860%29%29%5E2+
sin%2845%29=sqrt%282%29%2F2
cos%2845%29=sqrt%282%29%2F2
sin%2860%29=sqrt%283%29%2F2
cos%2860%29=1%2F2
you can finish it same way as above