Question

Proof:

i. Sec4A (1 - sin4A) - 2tan2A = 1

ii. tanθ/(secθ - 1) = (tanθ + secθ +1)/(tanθ + secθ - 1)

Answer 1

L.H.*. = sec4 A (1 – sin4 A) – 2 tan2 A

= sec4 A [12 – (sin2 A)2 ] – 2 tan2 A

= sec4 A (1 – sin2 A) (1 + sin2 A) – 2 tan2 A

= sec4 A cos2 A (1 + sin2 A) – 2 tan2 A [ ∵ sin θ + cos θ = 1 , ∵ 1 – sin θ = cos θ]