Question

3 ${\sin }^{2}x+4{\cos }^{2}x\in$

• A. [0,3]
• B. [0,4]
• C. [3,4]
• D. $[-4,-3]$

Answer 1

The correct option is C [3,4]

$f\left(x\right)=3{\sin }^{2}x+4{\cos }^{2}x$
$=3+co{s}^{2}x$
Now, $-1\le \cos x\le 1$.

So, $0\le {\cos }^{2}x\le 1$

So, $(0+3)\le {\cos }^{2}x+3\le (1+3)$

Range of $f\left(x\right)ϵ[3,4]$