write in trig expressions in terms of sine cosine and then s

write in trig expressions in terms of sine, cosine, and then simplify

cot/sin-csc

Solution

cotx/( sinx - cscx)

we know cotx = cosx/sinx ; cscx = 1/sinx

So, cotx/( sinx - cscx) = cosx/sinx /( sinx - 1/sinx)

= cosx/(sin^2x - 1)

= cosx/- cos^2x

= -1/cosx

= -secx