Question 692226
{{{((sin( pi/3) - cos (5pi/6))/(1 - tan( 3pi/4)cot( pi/4)))}}}
{{{sin(pi/3)}}} {{{pi/3}}} is a special angle. We should know that its sin is {{{sqrt(3)/2}}}
{{{cos (5pi/6)}}} {{{5pi/6}}} is also special angle. (<i>Any</i> integer multiple of {{{pi/6}}} is a special angle.) The reference angle is {{{pi/6}}} and the cos of this is {{{sqrt(3)/2}}}. Since {{{5pi/6}}} is in the second quadrant and cos is negative there, {{{cos(5pi/6) = -sqrt(3)/2}}}
{{{tan(3pi/4)}}} {{{3pi/4}}} is also special angle. (<i>Any</i> integer multiple of {{{pi/4}}} is a special angle.) The reference angle is {{{pi/4}}} and the tan of this is 1. Since {{{3pi/4}}} is in the second quadrant and tan is negative there, {{{tan(3pi/4) = -1}}}
{{{cot(pi/4)}}} {{{pi/4}}} is a special angle. We should know that its cot is 1.
Substituting in all these values into your expression we get:
{{{((sqrt(3)/2)-(-sqrt(3)/2))/(1-(-1)(1)))}}}
which simplifies as follows:
{{{((sqrt(3)/2)+(sqrt(3)/2))/(1-(-1)))}}}
{{{((2sqrt(3)/2)/2)}}}
{{{((cross(2)sqrt(3)/cross(2))/2)}}}
{{{(sqrt(3)/2)}}}