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

Question

1918 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-25T07:02:57

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

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 $csc(0+pi/6)=csc(pi/6)=2$

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