Question

I : Maximum value of $\sqrt{3}\sin x-\cos x$ is $2.$
II : Minimum value of $9{\tan }^{2}x+16{\cot }^{2}x$ is $24.$

• A. Only II is true
• B. Both I and II are true
• C. Only I is true
• D. Neither I nor II is true

Answer 1

The correct option is B Both I and II are true

I.
Maximum value of $asinx+bcosx+c$ is $c+\sqrt{a^2+b^2}$
Here $a=\sqrt{3},b=-1$, maximum value $=2$

True.
II.
By A.M - G.M inequality
$\frac{a+b}{2}\ge \sqrt{ab}$
$9{\tan }^{2}x+16{\cot }^{2}x\ge 2\times \sqrt{9{\tan }^{2}x\cdot 16{\cot }^{2}x}=24$
Minimum Value is $24$
$\Rightarrow$ Both are True.