Question #1a1ed

1 Answer
sente
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#

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