Question

Tan²A-Tan²B=Sin²A-Sin²B÷Cos²A×Cos²B

Answer 1

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

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Answer 2

Step-by-step explanation:

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