what will be the gradiesnt of f(x)=1 / sin(x - 90) where 100

Note that  sin(x - 90)    =  sinxcos90 - sin90cos x =  -cosx

So we have :

f(x)   = -1/cosx   = -secx

f ' (x)  = -sec(x)tan(x)

Look at the graph of the derivative here : https://www.desmos.com/calculator/4mdr48rapz

Note that the derivative [gradient ] is always negative on 100 < x < 180