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The simplified value of (see x sec y + tan x tan y)² – (sex x tan y + tan x sec y)² is :
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- - 1
- 0
- sec² x
- 1
Correct Option: D
(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 – 2 sec 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
