If sec x + tan x = 2 . then wat is the value of sec x

1) By identity, sec²x - 1 = tan²x

==> tan(x) = ±√(sec²x - 1)

2) So, ±√(sec²x - 1) = 2 - sec(x)

3) Squaring both sides, (sec²x - 1) = 4 - 4sec(x) + sec²x

simplifying, 4sec(x) = 5

Hence, sec(x) = 5/4

∵ sec x + tan x = 2 ......... and ( s + t )( s - t ) = 1

∴ sec x - tan x = 1/2

∴ adding : 2 sec x = 2 + 1/2

∴ sec x = 5/4 ................................ Ans.
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