The simplified value of (sec x sec y + tan x tan y)² - (sec x tan y + tan x sec y)²

A. -1

B. 0

C. sec² x

D. 1

Answer: Option D

Solution(By Examveda Team)

(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