Determine the values of x for which the given function is un

Determine the values of x for which the given function is undefined. (Let k be any integer.)

1) y = tan x

2) y = csc x

Solution

1) y = tan x

for x = pi/2;

tan(pi/2) = undefined

x = pi/2, 3pi/2 , 5pi/2....

x= (2k+1)pi/2    where k is any integer ; k=0, 1, 2...

2) y = cscx

for x= 0 ; cscx = undefined

cscx = 1/sinx = undefined

sinx = 0

x = 0,pi, 2pi,3pi....

x= k*pi

2) y = csc x where k is any integer ; k=0, 1, 2...