Question

Minimum value of $\frac{1}{3\sin \theta -4\cos \theta +7}$ is

• A. $\frac{1}{12}$
• B. $\frac{5}{12}$
• C. $\frac{7}{12}$
• D. $\frac{1}{6}$

Answer 1

The correct option is A $\frac{1}{12}$

$\mu$ in value of $\frac{1}{3\sin \theta -4\cos \theta +7}$

for this we need to find mass value of denominator

For any equation like

$a\sin \theta +b\cos \theta$

$\Rightarrow$ Rang is $[-\sqrt{a^2+b^2},\sqrt{a^2+b^2}]$

$\therefore$ here, range of $3\sin \theta -4\cos \theta +7$ is

$[-\sqrt{3^2+(-4{)}^2}+7,\sqrt{3^2+(-4{)}^2}+7]$

$\Rightarrow [2,12]$

$\therefore$ maximum value of den is $12$

$\Rightarrow$ Min value of this eqn is $\frac{1}{12}$