Trigonometric EquationHard
Question
If 0 < x < π and cosx + sinx = 
, then tanx is
, then tanx isOptions
A.
B.
C.-
D.
Solution
cos x sinx = 
⇒ 1 + sin2x = 
⇒ sin2x = - 
, so x is obtuse and 
⇒ 3tan2x 8tanx + 3 = 0
∴ tan x =
∵ tan x < 0 ∴ tan x =
⇒ 1 + sin2x = ⇒ sin2x = - , so x is obtuse and ⇒ 3tan2x 8tanx + 3 = 0∴ tan x =
∵ tan x < 0 ∴ tan x =
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