If $\alpha,-\frac{\pi}{2}<\alpha<\frac{\pi}{2}$ is the solution of $4 \cos \theta+5 \sin \theta=1$, then the value of $\tan \alpha$ is

  • [JEE MAIN 2024]
  • A

    $\frac{10-\sqrt{10}}{6}$

  • B

     $\frac{10-\sqrt{10}}{12}$

  • C

     $\frac{\sqrt{10}-10}{12}$

  • D

    $\frac{\sqrt{10}-10}{6}$

Similar Questions

The value of the expression

$\frac{{\left (sin 36^o + cos 36^o - \sqrt 2  sin 27^o)( {\sin {{36}^0} + \cos {{36}^0} - \sqrt 2 \sin {{27}^0}} \right)}}{{2\sin {{54}^0}}}$ is less than

Number of principal solution of the equation $tan \,3x - tan \,2x - tan\, x = 0$, is

The equation ${\sin ^4}x + {\cos ^4}x + \sin 2x + \alpha = 0$ is solvable for

If $\cos 2\theta = (\sqrt 2 + 1)\,\,\left( {\cos \theta - \frac{1}{{\sqrt 2 }}} \right)$, then the value of $\theta $ is

The solution set of $(5 + 4\cos \theta )(2\cos \theta + 1) = 0$ in the interval $[0,\,\,2\pi ]$ is