Question 84895
{{{cot (135)=cos(135)/sin(135)=(-sqrt(2)/2)/(sqrt(2)/2)=cross(-sqrt(2)/2)*cross(2/sqrt(2))=-1}}}


So you are correct {{{cot (135)=-1}}}


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{{{cos(pi/12)=cos(pi/3-pi/4)}}} Break up the argument. Note: {{{pi/3-pi/4=4pi/12-3pi/12=1pi/12=pi/12}}}


Now use the trig identity:

{{{cos(A-B)=cos(A)cos(B)+sin(A)sin(B)}}}


{{{cos(pi/3-pi/4)=cos(pi/3)cos(pi/4)+sin(pi/3)sin(pi/4)}}} Plug in {{{A=pi/3}}} and {{{B=pi/4}}}


Now using the unit circle, we get {{{cos(pi/3)=1/2}}}, {{{cos(pi/4)=sqrt(2)/2}}}, {{{sin(pi/3)=sqrt(3)/2}}}, and {{{sin(pi/3)=sqrt(2)/2}}}



{{{cos(pi/3-pi/4)=(1/2)(sqrt(2)/2)+(sqrt(3)/2)(sqrt(2)/2)}}} Substitute each trig function with it's corresponding expression



{{{cos(pi/3-pi/4)=sqrt(2)/4+sqrt(6)/4}}} Multiply


{{{cos(pi/3-pi/4)=(sqrt(2)+sqrt(6))/4}}} Combine the fractions


So 

{{{cos(pi/12)=(sqrt(2)+sqrt(6))/4}}}