Evaluate cot(arcos(1-1/x)) ?

Question

the answer should be an expression involving x

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Answer 1 · 2018-05-07T04:11:15

# (x-1)/sqrt(2x-1)#.

If #arc cos(1-1/x)=theta," then, "costheta=1-1/x#.

#:." The reqd. value"=cottheta#,

#=costheta/sintheta#,

#=costheta/sqrt(sin^2theta)#,

#=costheta/sqrt(1-cos^2theta)#,

#=(1-1/x)/{sqrt(1-(1-1/x)^2}#,

#=(x-1)/x-:sqrt{1-(x-1)^2/x^2}#,

#=(x-1)/x-:sqrt{x^2-(x-1)^2}/x#,

#=(x-1)-:sqrt{x^2-(x^2-2x+1)}#.

# rArr cot(arc cos(1-1/x))=(x-1)/sqrt(2x-1)#.

Enjoy Maths.!