Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
cosec x = [tex]\frac{1}{sinx}[/tex] , cot x = [tex]\frac{cosx}{sinx}[/tex]
Consider the left side
[tex]\frac{(1+cosA)^2-(1-cosA)^2}{sin^2A}[/tex] ← expand and simplify numerator
= [tex]\frac{1+2cosA+cos^2A-(1-2cosA+cos^2A}{sin^2A}[/tex]
= [tex]\frac{1+2cosA+cos^2A-1+2cosA-cos^2A}{sin^2A}[/tex]
= [tex]\frac{4cosA}{sin^2A}[/tex]
= 4 × [tex]\frac{1}{sinA}[/tex] × [tex]\frac{cosA}{sinA}[/tex]
= 4cosecAcotA
= right side, thus proven
