Question #1a1ed

1 Answer
Oct 25, 2016

x=sqrt(3)/3

Explanation:

"arccot"(x) + 2arcsin(sqrt(3)/2) = pi

The inverse sine function arcsin(x) is defined as the unique value in the interval [-pi/2,pi/2] such that sin(arcsin(x)) = x. On that interval, we have sin(pi/3) = sqrt(3)/2 as a well known angle. Thus arcsin(sqrt(3)/2) = pi/3

=> "arccot"(x) + (2pi)/3 = pi

=> "arccot"(x) = pi/3

=> cot("arccot"(x)) = cot((pi)/3)

=> x = cot((pi)/3)

=cos((pi)/3)/sin((pi)/3)

=(1/2)/(sqrt(3)/2)

=1/sqrt(3)

=sqrt(3)/3