# Prove the followi

LHS = (secx sec y + tanx tan y)2 – (secx tan y + tanx sec y)2

= [(secx sec y)2 + (tanx tan y)2 + 2 (secx sec y) (tanx tan y)] – [(secx tan y)2 + (tanx sec y)2 + 2 (secx tan y) (tanx sec y)]

= [sec2x sec2 y + tan2x tan2 y + 2 (secx sec y) (tanx tan y)] – [sec2x tan2 y + tan2x sec2 y + 2 (sec2x tan2 y) (tanx sec y)]

= sec2x sec2 y - sec2x tan2 y + tan2x tan2 y - tan2x sec2 y

= sec2x (sec2 y - tan2 y) + tan2x (tan2 y - sec2 y)

= sec2x (sec2 y - tan2 y) - tan2x (sec2 y - tan2 y)

We know that sec2x – tan2x = 1.

= sec2x × 1 – tan2x × 1

= sec2x – tan2x

= 1

= RHS

Hence proved.

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