Question

Show that (1/cos ∅) - cos ∅ = tan ∅ .sin ∅

Answer 1

LHS = (1/cos ∅) - cos ∅
= (1 - cos²∅)/cos ∅
= sin² ∅/cos∅
= (sin∅/cos∅) × sin∅
= tan ∅ .sin ∅
= RHS

hence proved!

here, (1-cos²A) = sin²A
sinA/cosA = tan A

Answer 2

(1/cos ∅) - cos ∅
= 1/cos ∅ - cos²∅/cos ∅
= (1-cos²∅)/cos ∅
= sin²∅/cos ∅
= tan ∅ × sin ∅

Hence proved