Question

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

Answer 1

`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`