(1+sinx/1+cosx)(1+secx/1+cosecx)=tanx

Question

Do please help solve

Answer 1

1+sec(x)=1+(1/cos(x))=(1+cos(x))/cos(x);

1+cosec(x)=1+(1/sin(x))=(1+sin(x))/sin(x).

Therefore we have:

[(1+sin(x))/(1+cos(x))][(1+cos(x))/cos(x))sin(x)/(1+sin(x))]=

(1/cos(x))sin(x)=sin(x)/cos(x)≡tan(x).

So this is not an equation to be solved but an identity to be proved true for all x.

The above workings prove the identity.

Answer 2

( 1 + sin x ) / ( 1 + cos x ) (1+ sec x ) / ( 1+ cosec x ) = tan x