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If tan x + sec x = √3, 0 < x < π, then x is equal toA. \(\cfrac{5\pi}6\)B. \(\cfrac{2\pi}3\)C. \(\cfrac{\pi}6\)D.\(\cfrac{\pi}3\) |
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Answer» Correct option is C. \(\cfrac{\pi}6\) 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 tan2 x (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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