Question

If f x cos sec x x 2 2 ^ h = + , then f x^ h

Answer 1

Answer:

sorry but I am in class 7 so I can't do this sum properly

Answer 2

We have:

f(x) = $\cos^2 x$ + $\sec^2 x$

We have to find, the range of f(x) = ?

Solution:

∴ $\cos^2 x$ + $\sec^2 x$

Since, $\cos^2 x$ and $\sec^2 x$ are positive.

Then, A.M.- G.M. can be applied.

We know that,

A.M. ≥ G.M.

∴ $\dfrac{\cos^2 x+\sec^2 x}{2}$ ≥  $\sqrt{\cos^2 x\sec^2 x}$

⇒ $\dfrac{\cos^2 x+\sec^2 x}{2}$ ≥  $\sqrt{\cos^2 x\dfrac{1}{\cos^2 x} }$

⇒ $\dfrac{\cos^2 x+\sec^2 x}{2}$ ≥  1

Multiplying both sides by 2, we get

⇒ $\cos^2 x+\sec^2 x$ ≥  2

⇒ f(x) ≥  2

∴ The range of f(x) = [2, ∞)

Thus, the range of f(x) is equal to [2, ∞).