The value of $\theta $ lying between $0$ and $\pi /2$ and satisfying the equation
$\left| {\,\begin{array}{*{20}{c}}{1 + {{\sin }^2}\theta }&{{{\cos }^2}\theta }&{4\sin 4\theta }\\{{{\sin }^2}\theta }&{1 + {{\cos }^2}\theta }&{4\sin 4\theta }\\{{{\sin }^2}\theta }&{{{\cos }^2}\theta }&{1 + 4\sin 4\theta }\end{array}\,} \right| = 0$
The value of $\theta $ lying between $0$ and $\pi /2$ and satisfying the equation
$\left| {\,\begin{array}{*{20}{c}}{1 + {{\sin }^2}\theta }&{{{\cos }^2}\theta }&{4\sin 4\theta }\\{{{\sin }^2}\theta }&{1 + {{\cos }^2}\theta }&{4\sin 4\theta }\\{{{\sin }^2}\theta }&{{{\cos }^2}\theta }&{1 + 4\sin 4\theta }\end{array}\,} \right| = 0$
- [IIT 1988]
- A
$\frac{{7\pi }}{{24}}$ or $\frac{{11\pi }}{{24}}$
- B
$\frac{{5\pi }}{{24}}$
- C
$\frac{\pi }{{24}}$
- D
None of these
Similar Questions
The number of real solutions of the equation $2 \sin 3 x+\sin 7 x-3=0$, which lie in the interval $[-2 \pi, 2 \pi]$ is
The number of real solutions of the equation $2 \sin 3 x+\sin 7 x-3=0$, which lie in the interval $[-2 \pi, 2 \pi]$ is
- [KVPY 2017]
If $\cos \theta = \frac{{ - 1}}{2}$ and ${0^o} < \theta < {360^o}$, then the values of $\theta $ are
If $\cos \theta = \frac{{ - 1}}{2}$ and ${0^o} < \theta < {360^o}$, then the values of $\theta $ are
If ${\tan ^2}\theta - (1 + \sqrt 3 )\tan \theta + \sqrt 3 = 0$, then the general value of $\theta $ is
If ${\tan ^2}\theta - (1 + \sqrt 3 )\tan \theta + \sqrt 3 = 0$, then the general value of $\theta $ is
The general solution of the trigonometric equation $\tan \theta = \cot \alpha $ is
The general solution of the trigonometric equation $\tan \theta = \cot \alpha $ is
The number of solutions of equation $3cos^2x - 8sinx = 0$ in $[0, 3\pi]$ is
The number of solutions of equation $3cos^2x - 8sinx = 0$ in $[0, 3\pi]$ is