Answer:
see explanation
Step-by-step explanation:
Consider the left side
[tex]\frac{cosA}{1-sinA}[/tex] + [tex]\frac{cosA}{1+sinA}[/tex]
= [tex]\frac{cosA(1+sinA)+cosA(1-sinA)}{(1-sinA)(1+sinA)}[/tex]
= [tex]\frac{cosA+cosAsinA+cosA-cosAsinA}{1-sin^2A}[/tex]
= [tex]\frac{2cosA}{cos^2A}[/tex] ← cancel cosA on numerator/ denominator
= 2 × [tex]\frac{1}{cosA}[/tex]
= 2secA
= right side, thus proven
