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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.

by Top Rated User (1.2m points)
( 1 + sin x ) / ( 1 + cos x ) (1+ sec x ) / ( 1+ cosec x ) = tan x
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