Question

please solve this.
Range of function f(x) = cos^2x + 4sec^2x is ?​

Answer 1

Answer:

[5, ∞)

Step-by-step explanation:

$f(x)=\cos^22x+4\sec^22x$

$\implies f(x)=\cos^22x+\frac{4}{\cos^22x}$

$\implies f(x)=\frac{(\cos^22x)^2+4}{\cos^22x}$

Since the minimum value of $\cos^42x$ is 0 and the maximum value is 1

Therefore, the minimum value of f(x) will be when  $\cos^22x$ is 1 and the maximum value will be when  $\cos^22x$ is 0

when  $\cos^22x$ is 1 then the value of f(x) = (1+4)/1 = 5

And when  $\cos^22x$ is 0 f(x) will be tending to infinity

Therefore, range of f(x) is [5, ∞)

Hope this is helpful.