Iy v (g o V™) (8 21T = v} (vgmo0 - 5% ot

1.	Iy v (g o V™) (8 21T = v} (vgmo0 - 5% ot
Answer» LHS: (tan^2 A - tan^2 B) = (sin^2 A/cos^2 A - sin^2 B/cos^2 B) = (sin^2 A.cos^2 B - sin^2 B.cos^2 A) /cos^2 A.cos^2 B = (1 - cos^2 A)cos^2 B - (1-cos^2 B)cos^2 A/cos^2 A. cos^2 B = (cos^2 B - cos^2 A.cos^2 B + cos^2 A.cos^2 B - cos^2 A)/cos^2 A.cos^2 B = (cos^2 B - cos^2 A)/cos^2 A.cos^2 B(firsrt proof) = (1 - sin^2 B) - (1 - sin^2 A)/ cos^2 A.cos^2 B = (sin^2 A - sin^2 B)/ cos^2 A.cos^2 B (second proof)

Answer»

LHS: (tan^2 A - tan^2 B)

= (sin^2 A/cos^2 A - sin^2 B/cos^2 B)

= (sin^2 A.cos^2 B - sin^2 B.cos^2 A) /cos^2 A.cos^2 B

= (1 - cos^2 A)cos^2 B - (1-cos^2 B)cos^2 A/cos^2 A. cos^2 B

= (cos^2 B - cos^2 A.cos^2 B + cos^2 A.cos^2 B - cos^2 A)/cos^2 A.cos^2 B

= (cos^2 B - cos^2 A)/cos^2 A.cos^2 B(firsrt proof)

= (1 - sin^2 B) - (1 - sin^2 A)/ cos^2 A.cos^2 B

= (sin^2 A - sin^2 B)/ cos^2 A.cos^2 B (second proof)

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