Question

A and B are acute angles of a right angled ∆ABC . Prove that tan²A - tan²B = sin²A- sin²B /cos²A x cos²B ​

Answer 1

Answer:

Step-by-step explanation:

A and B are acute angle of a right angled triangle

Therefore,90+A+B=180 degree

A+B=90

B=90-A......1

Substituting 1 in the question

LHS

Tan^2 A - tan^2 (90-A)

Tan^2 A - cot^2 A

Sin^2 A - cos^2 A/sin^2 A cos^2 A

RHS

sin^2 A - sin^2 (90-A)/cos^2 A × cos^2 (90-A)

sin^2 A - cos^2 A/ cos^2 A × sin^2 A

LHS=RHS

HENCE PROVED