Question

Simplifica:

1 + sec θ
--------------------
sen θ + tan θ


1 1
------------- + ---------------
1 + sen θ 1 - sen θ

Answer 1

1.)
${\dfrac{1+\sec x}{\sin x+\tan x}=}\\\\\\{\dfrac{1+\frac{1}{\cos x}}{\sin x+\frac{\sin x}{\cos x}}=}\\\\\\{\dfrac{\frac{\cos x +1}{\cos x}}{\frac{\sin x.\cos x+\sin x}{\cos x}}=}\\\\\\{\dfrac{\cos x +1}{\sin x (\cos x+1)}=}\\\\\\{\dfrac{1}{\sin x}=}\\\\{\boxed{\csc x}}$