(Cos theta) / (cos theta -sin theta)= (1/1-tan theta)

Question

establish the identity.

write the left side as an equivalent expression with 1 in the numerator 

Answer 1

I'm going to use x in place of θ.

prove:

cosx/(cosx-sinx)=(1/(1-tanx))

divide top and bottom by cosx

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

(1/([cosx/cosx]-[sinx/cosx])=

1/(1-tanx)

now replace the x's with θ's