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