QJEEM24Maf3a9: JEE Main 2024 Mathematics - Class 11 JEEM24Maf3a9 Solution: If is the solution of , then the value of is

Question

Verified Solution • 2025–26 Session moderate

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

Accepted Answer

$4+5 \tan \theta=\sec \theta$

Squaring : $24 \tan ^2 \theta+40 \tan \theta+15=0$

$\tan \theta=\frac{-10 \pm \sqrt{10}}{12}$

and $\tan \theta=-\left(\frac{10+\sqrt{10}}{12}\right)$ is Rejected.

(3) is correct.

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