Question 1047986
.
2 sin 112.5° cos 112.5°=?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
{{{2sin(alpha)*cos(alpha)}}} = {{{sin(2alpha)}}}

is well known trigonometry formula (see the lesson <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometric-functions-of-multiply-argument.lesson>Trigonometric functions of multiply argument</A> in this site, for example).


Therefore,

2 sin 112.5° cos 112.5°= = sin(2*112.5°) = sin(225°) = {{{-sqrt(2)/2}}}.


<U>Answer</U>.  2 sin 112.5° cos 112.5° = {{{-sqrt(2)/2}}}.
</pre>