Simplify the given expressions csct CSC Solution1 cscpi2 t

Simplify the given expressions.

Solution

1. csc(pi/2 - t)

csc theta=1/sin theta

csc(pi/2 - t) = 1/sin(pi/2 - t)

And sin(pi/2 - theta)= cos theta

Therefore sin(pi/2 - t) = cos t

1/sin(pi/2 - t) = 1/cos t=sect

2. cot(3pi/2 - x)

cot theta=1/tan theta

cot(3pi/2 -x)=1/tan(3pi/2 - x)

tan (3pi/2 - x) = cot x

1/tan(3pi/2 - x)=1/cotx = tan x