Question

Prove the following: 

i. sec θ (1 – sin θ) (sec θ + tan θ) = 1

ii. (sec θ + tan θ) (1 – sin θ) = cos θ

Answer 1

Proof: 

i. L.H.S. = sec θ (1 – sin θ) (sec θ + tan θ)

= 1

= R.H.S.

∴ sec θ (1 – sin θ) (sec θ + tan θ) = 1

ii. L.H.S. = (sec θ + tan θ) (1 – sin θ)

= cos θ

= R.H.S.

∴ (sec θ + tan θ) (1 – sin θ) = cos θ