1. sin(x) * (1 + tan(x))+ cos(x) * (1 + cot(x))

Question

2. (1 - cos²(x)) * (1 + tan²(x))

Answer 1

#1. recall the definitions of tanx and cotx
sin(x) * (1 + sin(x)/cos(x))+ cos(x) * (1 + cos(x)/sin(x))
expand and you will find that several terms can be simplified
#2. Try these identities
1 - cos²(x) = sin²(x)
1 + tan²(x) = sec²(x)

Answer 2

Okay, thank you.