Proving Trig identities Problems that need correction

Here are some more problems that need checking from my other thread I made.

1) $\displaystyle sin x * tan x + cos x$

$\displaystyle sin x * (sin x ) / (cos x) + cos x$

$\displaystyle (sin x ^ 2) / (cos x) + cos x = Answer: sin x ^ 2 $

2) $\displaystyle (1)/ (1 + cos x) + (1 ) / (1 - cos x) = $

$\displaystyle (1 - cos x) / (1 + cos x) + (1 + cos x) / (1 - cos x =

Answer: (2)/(2) = 1 $

)

For this problem, does it matter if the right side's answer is the same value on the left side but flipped?

3) $\displaystyle sin t * tan t = 1 - cos ^ 2 t / cos t $

Doing the right side:

$\displaystyle sin ^ 2 t/ cos t $

$\displaystyle (sin t) / (cos t) * sin t $

$\displaystyle Answer: tan t * sec t $