If sec(x)+tan(x)=2012, then 2011(csc(x)+cot(x))?

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Answer 1 · 2017-10-21T02:08:20

Given

#secx+tanx=2012.....(1)#

So

#secx-tanx=(sec^2x-tan^2x)/(secx+tanx)#

#=>secx-tanx=1/2012.....(2)#

Adding (1) and (2) we get

#secx=1/2(2012+1/2012)....(3)#

Subtracting (2) from (1) we get

#tanx=1/2(2012-1/2012).....(4)#

so dividing (3) by (4) we get

#secx/tanx=(2012+1/2012)/(2012-1/2012)#
#=>cscx=(2012^2+1)/(2012^2-1)#

Now

#2011(cscx+cotx)#

#=2011(cscx+1/tanx)#

#=2011((2012^2+1)/(2012^2-1)+(2*2012)/(2012^2-1))#

#=2011((2012+1)^2/(2012^2-1))#

#=2011xx(2013)^2/(2013*2011)#

#=2013#