Question

Prove this (sinx-tanx)(cosx-cotx)=(sinx-1)(cosx-1)

Answer 1

distribute first
sinx cosx - sinx cotx - cosx tanx+tanx cotx
sinx cosx - sinx (cosx/sinx) - cosx (sinx/cosx) + tanx (cosx/sinx)
sinxcosx - cosx - sinx +1
and factor
cosx(sinx -1) -1(sinx - 1)
(sinx -1)(cosx-1)

Answer 2

(sinx−tanx)(cosx−cotx)

=(sinx−sinxcosx)(cosx−cosxsinx)

=sinx(1−1cosx)cosx(1−1sinx)

=sinx(cosxcosx−1cosx)cosx(sinxsinx−1sinx)

=sinxcosx(cosx−1)cosxsinx(sinx−1)

=(cosx−1)(sinx−1)