The value of $\theta$ lying between $\theta = 0$ and $\theta = \pi /2$ and satisfying the equation : $\left| {\,\begin{array}{*{20}{c}} {1\,\, + \,\,{{\sin }^2}\,\theta }&{{{\cos }^2}\,\theta }&{4\,\sin \,4\,\theta }\\ {{{\sin }^2}\,\theta }&{1\,\, + \,\,{{\cos }^2}\,\theta }&{4\,\sin \,4\,\theta }\\ {{{\sin }^2}\,\theta }&{{{\cos }^2}\,\theta }&{1\,\, + \,\,4\,\sin \,4\,\theta } \end{array}\,} \right|$ $= 0$ are :
The value of $\theta$ lying between $\theta = 0$ and $\theta = \pi /2$ and satisfying the equation : $\left| {\,\begin{array}{*{20}{c}} {1\,\, + \,\,{{\sin }^2}\,\theta }&{{{\cos }^2}\,\theta }&{4\,\sin \,4\,\theta }\\ {{{\sin }^2}\,\theta }&{1\,\, + \,\,{{\cos }^2}\,\theta }&{4\,\sin \,4\,\theta }\\ {{{\sin }^2}\,\theta }&{{{\cos }^2}\,\theta }&{1\,\, + \,\,4\,\sin \,4\,\theta } \end{array}\,} \right|$ $= 0$ are :
- A
$\frac{{7\,\pi }}{{24}}$
- B
$\frac{{5\,\pi }}{{24}}$
- C
$\frac{{11\,\pi }}{{24}}$
- D
both $(A)$ and $(C)$
Similar Questions
If $p, q, r, s$ are in $A.P.$ and $f (x) =$ $\left| {\,\begin{array}{*{20}{c}}
{p\,\, + \,\,\sin \,x}&{q\,\, + \,\,\sin \,x}&{p\,\, - \,\,r\,\, + \,\,\sin \,x}\\
{q\,\, + \,\,\sin \,x}&{r\,\, + \,\,\sin \,x}&{ - \,1\,\, + \,\,\sin \,x}\\
{r\,\, + \,\,\sin \,x}&{s\,\, + \,\,\sin \,x}&{s\,\, - \,\,q\,\, + \,\,\sin \,x}
\end{array}\,} \right|$ such that $f (x)dx = - 4$ then the common difference of the $A.P.$ can be :
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