Answer:
see explanation
Step-by-step explanation:
Using the identity
sin²A = 1 - cos²A , tanA = [tex]\frac{sinA}{cosA}[/tex]
Consider the left side
tan²A - sin²A
= [tex]\frac{sin^2A}{cos^2A}[/tex] - sin²A
[tex]\frac{sin^2A-sin^2Acos^2A}{cos^2A}[/tex]
= [tex]\frac{sin^2A(1-cos^2A)}{cos^2A}[/tex]
= [tex]\frac{sin^2A.sin^2A}{cos^2A}[/tex]
= sin²A × [tex]\frac{sin^2A}{cos^2A}[/tex]
= sin²A . tan²A
= right side , thus verified
