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The simplified value of (sec x sec y + tan x tan y)2 - (sec x tan y + tan x sec y)2
Answer & Solution
Correct Answer:
Option
D
(sec x sec y + tan x tan y)2 - (sec x tan y + tan x sec y)2
= sec2x. sec2y + tan2x. tan2y + 2sec x. sec y. tan x. tan y - sec2x. tan2y - tan2x. sec2y + 2sec x. tan y. tan x sec y
= sec2x [sec2y - tan2y] - tan2x [sec2y - tan2y]
= (sec2x - tan2x) (sec2y - tan2y)
= 1 × 1
= 1
= sec2x. sec2y + tan2x. tan2y + 2sec x. sec y. tan x. tan y - sec2x. tan2y - tan2x. sec2y + 2sec x. tan y. tan x sec y
= sec2x [sec2y - tan2y] - tan2x [sec2y - tan2y]
= (sec2x - tan2x) (sec2y - tan2y)
= 1 × 1
= 1
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