Question

TAN^2 A-TAN^2 B=SIN^2 A - SIN^2 B/COS^2 A.COS^2 B

Answer 1

Please see the attached file.

Answer 2

L:H:S ≡ tan²A - tan²B

⇒ use tan²x = sec²x -1

= sec²A - 1 - (sec²B - 1)

= sec²A - 1 - sec²B +1

= sec²A - sec²B

= 1/cos²A - 1/cos²B

= (cos²B - cos²A)/cos²A.cos²B

⇒ use cos²x =1 - sin²x

= (1-sin²B -1 + sin²A)/cos²A.cos²B

= (sin²A - sin²B)/cos²A.cos²B

Hence L:H:S ≡ R:H:S