Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identity
sin²x + cos²x = 1 , then
sin²x = 1 - cos²x and cos²x = 1 - sin²x
Consider the left side
[tex]\frac{(1-sinA)(1 + sinA)}{(1+cosA)(1-cosA)}[/tex] ← expand numerator/denominator using FOIL
= [tex]\frac{1-sin^2A}{1-cos^2A}[/tex]
= [tex]\frac{1-(1-cos^2A)}{1-(1-sin^2A)}[/tex]
= [tex]\frac{1-1+cos^2A}{1-1+sin^2A}[/tex]
= [tex]\frac{cos^2A}{sin^2A}[/tex]
= cot²A = right side , thus proven
