SOLUTION: Please explain Evaluate the expression without using a calculator: {{{ (sin (pi/4) cos (pi/6) - sin (pi/6) cos (pi/4))^2 }}} THANKS

Algebra ->  Trigonometry-basics -> SOLUTION: Please explain Evaluate the expression without using a calculator: {{{ (sin (pi/4) cos (pi/6) - sin (pi/6) cos (pi/4))^2 }}} THANKS      Log On


   

Question 929033: Please explain
Evaluate the expression without using a calculator:
+%28sin+%28pi%2F4%29+cos+%28pi%2F6%29+-+sin+%28pi%2F6%29+cos+%28pi%2F4%29%29%5E2+

THANKS
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
+%28sin+%28pi%2F4%29+cos+%28pi%2F6%29+-+sin+%28pi%2F6%29+cos+%28pi%2F4%29%29%5E2+
***
rearrange terms:
%28sin%28pi%2F4%29cos%28pi%2F6%29-cos%28pi%2F4%29%29sin%28pi%2F6%29%5E2
Identity: sin(x-y)=sinxcosy-cosxsiny)

(sin (pi/4)cos(pi/6)-sin(pi/6)cos(pi/4))^2=sin^2(π/12)