Question

The maximum value of $4{\sin }^{2}x+3{\cos }^{2}x$ is

• A. $3$
• B. $4$
• C. $5$
• D. $7$

Answer 1

Answer: (B)

$4$

Let $f=4{\sin }^{2}x+3{\cos }^{2}x$

$\Rightarrow f=4{\sin }^{2}x+3(1-{\sin }^{2}x)$

$\Rightarrow f=4{\sin }^{2}x+3-3{\sin }^{2}x$

$\Rightarrow f={\sin }^{2}x+3$

We know that $3$ is a constant and maximum value of $\sin x=1$

Thus, the maximum value of the given expression can be

$f_{max}=3+{\left(1\right)}^2=3+1=4$