Step-by-step explanation:
3. (1 + cos x) (1 − cos x)
Distribute using FOIL.
1 − cos²x
Use Pythagorean identity.
sin²x
4. sin x / (1 − cos x)
Multiply by the conjugate.
sin x (1 + cos x) / ((1 − cos x) (1 + cos x))
Distribute using FOIL.
sin x (1 + cos x) / (1 − cos²x)
Use Pythagorean identity.
sin x (1 + cos x) / sin²x
Divide.
(1 + cos x) / sin x.
Split the fraction.
(1 / sin x) + (cos x / sin x)
csc x + cot x
