$\alpha=\sin 36^{\circ}$ is a root of which of the following equation

  • [JEE MAIN 2022]
  • A

    $10 x^{4}-10 x^{2}-5=0$

  • B

    $16 x^{4}+20 x^{2}-5=0$

  • C

    $16 x^{4}-20 x^{2}+5=0$

  • D

    $16 x^{4}-10 x^{2}+5=0$

Similar Questions

The solution of the equation $\left| {\,\begin{array}{*{20}{c}}{\cos \theta }&{\sin \theta }&{\cos \theta }\\{ - \sin \theta }&{\cos \theta }&{\sin \theta }\\{ - \cos \theta }&{ - \sin \theta }&{\cos \theta }\end{array}\,} \right| = 0$, is

The general solution of ${\sin ^2}\theta \sec \theta + \sqrt 3 \tan \theta = 0$ is

$cos (\alpha \,-\,\beta ) = 1$ and $cos (\alpha  +\beta ) = 1/e$ , where $\alpha , \beta \in [-\pi , \pi ]$ . Number of pairs of $(\alpha ,\beta )$ which satisfy both the equations is

If the sum of solutions of the system of equations $2 \sin ^{2} \theta-\cos 2 \theta=0$ and $2 \cos ^{2} \theta+3 \sin \theta=0$ in the interval $[0,2 \pi]$ is $k \pi$, then $k$ is equal to.

  • [JEE MAIN 2022]

If $\mathrm{n}$ is the number of solutions of the equation

$2 \cos x\left(4 \sin \left(\frac{\pi}{4}+x\right) \sin \left(\frac{\pi}{4}-x\right)-1\right)=1, x \in[0, \pi]$

and $S$ is the sum of all these solutions, then the ordered pair $(\mathrm{n}, \mathrm{S})$ is :

  • [JEE MAIN 2021]