Question

I: The greatest value of the function $f\left(x\right)=si{n}^{2}x-20cosx+1$ is 25
II : The minimum value $of\frac{7}{4\sin x+3\cos x+2}$ is 1 which of the above statements are true ?

• A. only I
• B. only II
• C. both I and II
• D. neither I nor II

Answer 1

Answer: (B)

only II

(I) $f^{\prime }\left(x\right)=2sinxcosx+20sinx$
$=2sinx(cosx+10)$
$f^{\prime }\left(x\right)>0$ If $x\in (o,\pi )$
$f^1\left(x\right)<0$ If $x\in (\pi ,2\pi )$
So $f\left(x\right)$ is maximum at $x=\pi$
$f\left(x\right)=21$
(II) $f\left(x\right)=\frac{7}{5sin(x+\theta )+2}$ where $tan\theta =\frac{3}{4}$

$f\left(x\right)$ is min when $sin(x+\theta )$ is max
$f\left(x\right)=\frac{7}{5+2}=1$