If f x -cos - 2 x - sec - 2 x- thenA- fx - 2B- f x -1C- f x -1D- 2- f x -1

The correct option is A f(x)≥ 2 Given that, f(x)=cos^2 x+sec^2 x We know that,AM ≥ GM =cos^2 x +sec^2x/2≥√(cos^2 x sec^2 x) ⇒ cos^2 x+sec^2 x ≥ 2 [∵ cos x. sec ...

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Byju's Answer

Standard XII

Mathematics

Range of Trigonometric Expressions

If f x =cos ∧...

Question

If f(x)=cos^2 x +sec^2 x, then

f(x)<1

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f(x)=1

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2 < f(x)< 1

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$f (x) \geq 2$

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Solution

The correct option is D
$f (x) \geq 2$

Given that, $f (x) = c o s^{2} x + s e c^{2} x$

We know that, $A M \geq G M$

$= \frac{c o s^{2} x + s e c^{2} x}{2} \geq \sqrt{c o s^{2} x s e c^{2} x}$

$\Rightarrow c o s^{2} x + s e c^{2} x \geq 2$

$[∵ c o s x . s e c x = 1]$

$\Rightarrow f (x) \geq 2$

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If f(x)=cos^2 x +sec^2 x, then

The correct option is D f(x)≥2 Given that, f(x)=cos2x+sec2x We know that,AM≥GM =cos2x+sec2x2≥√cos2xsec2x ⇒cos2x+sec2x≥2 [∵cosx.secx=1] ⇒f(x)≥2