Question

prove that tan(x)/sin(x)=sec(x)

Answer 1

tanx
-------
sin x

sin x
--------
cos x
--------
sin x

cancel sin x

1
-----
cos x

this becomes sec x

Answer 2

Answer:

$\frac{tan\left(x\right)}{sin\left(x\right)}=\frac{\frac{sin\left(x\right)}{cos\left(x\right)}}{sin\left(x\right)}=\frac{sin\left(x\right)}{cos\left(x\right)\cdot sin\left(x\right)}=\frac{1}{cos\left(x\right)}=sec\left(x\right)$ QED.

Step-by-step explanation: