Question

Prove the identity (1+secx )(cosec x- cot x) = tan x.

Answer 1

Step-by-step explanation:

if we consider L.H.S

=(1+secx)(cosecx-cotx)

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

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

=(1-(cos^2(x))/cosxsinx

=sin^2(x)/cosxsinx

=sinx/cosx

=tanx

hence L.H.S=R.H.S