UPSC NDA I 2019 Mathematics Solved Paper

(A)
Given trigonometric expression can be written as
1 + tan‌2 α tan‌2 β + 2 tan α tan β + tan‌2 α + tan‌2 β − 2 tan α tan β − sec‌2 α .sec‌2 β
= (1+tan‌2 α)(1+tan‌2 β) − sec‌2 α sec‌2 β
= sec‌2 α sec‌2 β − sec‌2 α sec‌2 β
= 0