The simplified value of $(sec x sec y + tan x tan y)^{2} - (sec x tan y + tan x sec y)^{2}$ is :
The simplified value of $(sec x sec y + tan x tan y)^{2} - (sec x tan y + tan x sec y)^{2}$ is :
1). -1
2). 0
3). $sec^{2}x$
4). 1
2 answers
(secx . secy + tanx . tany)2 –(sec x . tan y + tan x . sec y)2
= sec2 x . sec2 y + tan2 x . tan2y +2 sec x . sec y . tan x . tan y –sec2 x . tan2 y – tan2 x . sec2y – 2sec x . sec y . tan x . tan y
= sec2 x . sec2y + tan2x . tan2 y –sec2 x . tan2y – tan2 x . sec2y
= sec2x . sec2y – sec2x . tan2y –tan2x . sec2y + tan2 x . tan2y
= sec2x (sec2y – tan2y) – tan2x(sec2y – tan2y)
= sec2x – tan2x = 1.
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