Question #f7708

1 Answer
Aug 15, 2017

Constant 1

Explanation:

first thing is: sin(pi/2 - y)sin(π2y) = cos(y)
Imagine y = 0. Then, sin(pi/2) = 1, which = cos(0)
y = pi/2π2, then sin(pi/2 - pi/2) = sin(0) = 0sin(π2π2)=sin(0)=0, which is cos(pi/2).

Carry this on long enough to satisfy yourself.

So then, sec (y) cos(y) = cos(y)/cos(y) = 1sec(y)cos(y)=cos(y)cos(y)=1
pdate: bear in mind that the function is undefined where cos(y) = 0. I.e,
y=pi/2, 3pi/2, etc.π2,3π2,etc. You can get as infinitesimally close as you want to these points, but exactly at them, the function is undefined.