prove that tan^2A - tan^2B = cos^2 B - cos^2 A / cos^2 B cos^2 A
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hello,
LHS=
tan²A-tan²B
using identity tan²A=sec²A-1
=sec²A-1-(sec²B-1)
=sec²A-1-sec²B+1
=sec²A-sec²B
=1/cos²A-1/cos²B
taking LCM
=(cos²B-cos²A)/cos²B·cos²A
hence proved
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LHS=
tan²A-tan²B
using identity tan²A=sec²A-1
=sec²A-1-(sec²B-1)
=sec²A-1-sec²B+1
=sec²A-sec²B
=1/cos²A-1/cos²B
taking LCM
=(cos²B-cos²A)/cos²B·cos²A
hence proved
hope this helps,if u like it please mark it as brainliest
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