If fx-1-cos 2 x-8 sin 2 x-sin 2 x- Then the minimum value of fx is

The correct option is C 4 f(x)=1+cos2x+8sin^2x/sin 2x =2cos^2x+8sin^2x/2sinx cos x =1+4tan^2x/tan x =1/tan x+4tan x Using A.M≥ G.M 1+4tan^2x/2tan x≥√(4) ⇒1/ ...

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Byju's Answer

Standard XII

Mathematics

Addition Rule of Differentiation

If fx=1+cos 2...

Question

If $f (x) = \frac{1 + c o s 2 x + 8 s i n^{2} x}{s i n 2 x}$ . Then the minimum value of f(x) is

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Solution

The correct option is C
4

$f (x) = \frac{1 + c o s 2 x + 8 s i n^{2} x}{s i n 2 x} = \frac{2 c o s^{2} x + 8 s i n^{2} x}{2 s i n x c o s x} = \frac{1 + 4 t a n^{2} x}{t a n x} = \frac{1}{t a n x} + 4 t a n x$
Using $A . M \geq G . M \frac{1 + 4 t a n^{2} x}{2 t a n x} \geq \sqrt{4} \Rightarrow \frac{1}{t a n x} + 4 t a n x \geq 4$

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If f(x)=1+cos2x+8sin2xsin 2x. Then the minimum value of f(x) is

The correct option is C 4 f(x)=1+cos2x+8sin2xsin 2x=2cos2x+8sin2x2sinx cos x=1+4tan2xtan x=1tan x+4tan x Using A.M≥G.M1+4tan2x2tan x≥√4⇒1tan x+4tan x≥4

If $f (x) = \frac{1 + c o s 2 x + 8 s i n^{2} x}{s i n 2 x}$ . Then the minimum value of f(x) is