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Show that (sec^2(x) - tan(x))/(sec^2(x) + tan(x)) lies between 1/3 and 3

Show that 
(sec^2(x) - tan(x))/(sec^2(x) + tan(x)) lies between 1/3 and 3

Grade:11

1 Answers

Lab Bhattacharjee
121 Points
8 years ago
\text{Let } y=\dfrac{\sec^2x-\tan x}{\sec^2x+\tan x}=\dfrac{1-\tan x+\tan^2x}{1+\tan x+\tan^2x} \\ \text{Rearrange to form a Quadratic Equation in }\tan x \\ \text{As } \tan x \text{ is real, the discriminant must be }\ge0
 

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