What is the simplification of the given function? #sec^(-1)[(2sqrt2)/(1+sqrt3) ]#

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Answer 1 · 2017-12-30T19:31:20

Either #sec^-1(sqrt6-sqrt2)# which is #secx=sqrt6-sqrt2# or

#cos^-1((sqrt2+sqrt6)/4)# which is #cosx=(sqrt2+sqrt6)/4#

.

#sec^-1((2sqrt2)/(1+sqrt3))#

#=sec^-1((2sqrt2(1-sqrt3))/(1-3))=sec^-1((2sqrt2(1-sqrt3))/-2)=#

#sec^-1(-sqrt2(1-sqrt3))=sec^-1(sqrt6-sqrt2)#

We know #secx=1/cosx#. As such, if we let this angle be #x# we will have:

#secx=(2sqrt2)/(1+sqrt3)#

#1/cosx=(2sqrt2)/(1+sqrt3)#

#cosx=(1+sqrt3)/(2sqrt2)=(sqrt2(1+sqrt3))/4=(sqrt2+sqrt6)/4#

#x=cos^-1((sqrt2+sqrt6)/4)#