Question #f7708

Aug 15, 2017

Constant 1

Explanation:

first thing is: $\sin \left(\frac{\pi}{2} - y\right)$ = cos(y)
Imagine y = 0. Then, sin(pi/2) = 1, which = cos(0)
y = $\frac{\pi}{2}$, then $\sin \left(\frac{\pi}{2} - \frac{\pi}{2}\right) = \sin \left(0\right) = 0$, which is cos(pi/2).

Carry this on long enough to satisfy yourself.

So then, $\sec \left(y\right) \cos \left(y\right) = \cos \frac{y}{\cos} \left(y\right) = 1$
pdate: bear in mind that the function is undefined where cos(y) = 0. I.e,
y=$\frac{\pi}{2} , 3 \frac{\pi}{2} , e t c .$ You can get as infinitesimally close as you want to these points, but exactly at them, the function is undefined.