Find the value of #tan(cos^(-1)(3/x))#?

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Answer 1 · 2017-10-24T17:11:24

#tan(cos^(-1)(3/x))=tant=1/3sqrt(x^2-9)#

Let #cos^(-1)(3/x)=t#

then #cost=3/x#

and therefore #sect=x/3#

and #sec^2x=x^2/9# and #tan^2t=x^2/9-1=(x^2-9)/9#

and #tant=1/3sqrt(x^2-9)#

hence #tan(cos^(-1)(3/x))=tant=1/3sqrt(x^2-9)#