What is the correct option from the following for, #3tanx+27cotx>=#?

Question

#a)24#
#b)18#
#c)50#

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Answer 1 · 2018-01-12T14:40:22

Let

#y=3tanx+27cotx#

#=>y=3((sqrttanx)^2+(3sqrtcotx)^2)#

#=>y=3((sqrttanx)-(3sqrtcotx))^2+2*3*sqrttanxsqrtcotx)#

#=>y=3((sqrttanx)-(3sqrtcotx))^2+2*3)#

As #(sqrttanx)-(3sqrtcotx))^2>=0#

#y>=3*2*3#

#=>3tanx+27cotx>=18#