Question

prove that tan²A + tan²B = sin²B - sin²A / sin²B*sin²A​

Answer 1

Answer:

first take common what else it comes

on both the sides

then solve

Answer 2

here you go:-

Step-by-step explanation:

tan²x = sin²x/cos²x, and sin²x + cos²x = 1 

tan²A - tan²B = sin²A/cos²A - sin²B/cos²B 

= sin²A cos²B/cos²A cos²B - sin²B cos²A/cos²A cos²B 

= sin²A(1-sin²B)/cos²A cos²B - sin²B(1-sin²A)/cos²A cos²B 

= (sin²A - sin²Asin²B)/cos²A cos²B - (sin²B - sin²Asin²B)/cos²A cos²B 

= (sin²A - sin²Asin²B) - (sin²B - sin²Asin²B)/cos²A cos²B 

= (sin²A - sin²Asin²B - sin²B + sin²Asin²B)/cos²A cos²B 

= (sin²A - sin²B)/cos²A cos²B