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Q12 pls asap brainliest question

Answer»

Tan X = √(sec² x - 1) = √{(SEC x + 1)(sec x - 1)}
so,LHS= tan x/(sec x - 1) =√{(sec x + 1)(sec x - 1)}/(sec x - 1)
=√{(sec x + 1)/(sec x - 1)}
=(sec x + 1)/√(sec²x -1)
=(sec x + 1)/tan x

RHS = tan x + sec x + 1/tan x + sec x - 1
= (tan²x+sec²x+1+2tan x sec x+2tan x +2sec x)/(tan²x+sec²x+2tan x sec x - 1)
=(2sec²x+2tan x sec x + 2tan x + 2sec x)/(2tan²x + 2tan x sec x)
=(sec x (1+sec x) + tan x ( 1 + sec x))/{tan x (tan x + sec x)}
=(sec x + 1)/tan x
so, LHS=RHS [SHOWED.]
[P.S.: Theta is denoted with "x" here.]


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