Q. 83.5( 4 Votes )

Mark the correct A.

B.

C.

D.

Answer :

Given: tan x + sec x = √3


squaring on both sides


(tan x + sec x)2 = √32


tan2x+sec2x+2 tan x sec x = 3


Also, sec2x - tan2x = 1


tan2x + 1+ tan2x+ 2tan x sec x = 3


2tan2x+2tan x sec x = 3-1


tan2x+tan x sec x = 2/2


tan2x+tan x sec x = 1


tan x sec x = 1 - tan2x


again, squaring on both sides


tan2x sec2x = 1 + tan4x - 2 tan2x


(1+ tan2x) tan2x = 1 + tan4x - 2 tan2x


Tan4x + tan2x = 1 + tan4x - 2 tan2x


3 tan2x = 1


tan x = 1/√3


x = π/6.

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