Write tan x in terms of sec x tan x plusminus squareroot se

Write tan x in terms of sec x. tan x = plusminus squareroot sec^2 x -1/sec x tan x = plusminus squareroot sec^2 x -1/sec^2 x -1 tan x = plusminus sec x squareroot sec^2 x -1/sec^2 x -1 tan x = plusminus squareroot sec^2 x -1

Solution

sec²x- tan²x=1

tan²x=sec²x-1

taking square root on both sides

sqrt(tan²x)= +-sqrt(sec²x - 1)

tan x=+- sqrt(sec²x -1)

The correct option is D