#"cosec"((nπ)/2+(-1)^n π/6)# is equal to? where #n in ZZ#

1 Answer
Jul 25, 2018

#csc((npi)/2+(-1)^npi/6)# can take values #-2,-2/sqrt3,2/sqrt3# and #2#

Explanation:

If #n# is odd, then #csc((npi)/2+(-1)^npi/6)# then

#csc((npi)/2-pi/6)# is equivalent to #csc(pi/2-pi/6)=csc(pi/3)=2/sqrt3#

or #csc((3pi)/2-pi/6)=csc(pi+pi/3)=-2/sqrt3#

and if #n# is even, then #csc((npi)/2+(-1)^npi/6)#

#csc(pi+pi/6)# is equivalent to #-csc(pi/6)=-2#

or #csc(0+pi/6)=csc(pi/6)=2#