Simplify so that no quotients appear in the final expression

Question

cos^2x-sin^2x / sinxcosx'?

answer choices: 

a. sinx-cosx 
b. tanx-cotx 
c. cotx-tanx 
d. -tanx(cotx) 
e. tanx 
f. cotx(tanx) 

Answer 1

The expression (cos²x - sin²x)/(sinx cosx)

= [cos²x/(sinx cosx)] -[sin²x/(sinx cosx)]

= (cosx/sinx) - (sinx/cosx)

= cotx - tanx

(cos²x - sin²x)/(sinx cosx) = cotx - tanx

Option c is correct.