Prove that: sec 2θ - cot 2(90º - θ ) = cos 2(90º- θ ) + cos 2θ.
L.H.S. = sec 2 θ - cot 2 (90º - θ )
= sec 2 θ - tan 2 θ
= 1 + tan 2 θ - tan 2 θ
( ∵ sec 2 θ = 1 + tan 2 θ)
= 1
R.H.S. = cos 2 (90° - θ) + cos 2 θ
= sin 2 θ + cos 2 θ
( ∵ sin 2 θ + cos 2 θ = 1)
= 1
L.H.S. = R.H.S.
∴ sec 2 θ - cot 2 (90º - θ ) = cos 2 (90º - θ ) + cos 2 θ.
AI is thinking…
Couldn't generate an explanation.
Generated by AI. May contain inaccuracies — always verify with your textbook.
