Using Trig Identities to see if derrivatives are equal

[keykar]

Homework Statement

for homework we have to find 2 different dirrivatives of the same problem (one may be incorrect) and then tell if they are equal

2. The attempt at a solution
original
y=sec(x)*cot(x)

the two derrivatives (i know these are correct becase i have compared with others in the class)

using product rule first
dy/dx=-sec(x)*cot^2(x)

using simplification first
dy/dx=-csc(x)*cot(x)

this is my question...is there any way u can find that -secx(cotx)^2=-cscxcotx ??

 

[jgens]

Sure. You should know that sec(x) = 1/cos(x) and that cot(x) = cos(x)/sin(x). Using these definitions we have that sec(x) * cot²(x) = (1/cos(x)) * (cos²(x)/sin²(x)) = . . .

 

[keykar]

Thx jgens! Ur a life saver