Help me to solve this problem about trigonometry please?

Question

#tan^(-1) x=cos^(-1) x#

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Answer 1 · 2017-09-15T02:01:01

See below.

Applying #tan# to both sides

#x = tan(cos^-1 x) = sqrt[1 - x^2]/x# or

#x^2=sqrt(1-x^2)# or

#x^4 = 1-x^2# and solving for #x^2# we have

#x^2=1/2 (sqrt[5]-1)# and finally

#x = pm sqrt(1/2 (sqrt[5]-1))#