Question

cos square A- cos square B/cos square A×cos square b=tan square B-tan square A​

Answer 1

Solution

L.H.S → (cos²A - cos²B)/cos²A cos²B

By separating both terms

→ cos²A/(cos²A cos²B) - cos²B/(cos²A cos²B)

Here the like terms cancel out

→ 1/cos²B - 1/cos²A

→ sec²B - sec²A [sec∅ = 1/cos∅]

Since sec²∅ = tan∅ + 1

→ tan²B + 1 - (tan²A + 1)

→ tan²B - tan²A = R.H.S

Hence Proved