Question

prove that:sin^2A-sin^2B=cos^2B-cos^2A​

Answer 1

$\huge\bold{\mathtt{\red{Solution :—}}}</p><p>$

→ L.H.S. = sin²A - sin²B

= ( 1 - cos² A) - ( 1 - cos²B)

= 1 - cos²A - 1 + cos²B

= - cos²A + cos²B

= cos²B - cos²A

$= \small\bold{\boxed {R.H.S.}}$

★ So, sin²A - sin²B = cos²B - cos²A

$\Large\bold{\colorbox{yellow}{\underline{\underline{♣Proved♣}}}}$

Formula used :—

$\large\bold{\boxed{sin²∅ + cos²∅ = 1 }}$