Question : If $\sqrt{3} \tan ^2 \theta-4 \tan \theta+\sqrt{3}=0$, then what is the value of $\tan ^2 \theta+\cot ^2 \theta$?
Option 1: $\frac{4}{3}$
Option 2: $\frac{10}{3}$
Option 3: $3$
Option 4: $\frac{6}{5}$
New: SSC CHSL tier 1 answer key 2024 out | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $\frac{10}{3}$
Solution : $\sqrt{3} \tan ^2 \theta-4 \tan \theta+\sqrt{3}=0$ Multiplying by $\sqrt{3}$ on both sides, we get, $3\tan^2\theta−4\sqrt{3}\tan \theta+3=0$ ⇒ $3\tan^2\theta−3\sqrt{3}\tan\theta−\sqrt{3}\tan\theta+3=0$ ⇒ $3\tan\theta(\tan\theta−\sqrt{3})−\sqrt{3}(\tan\theta−\sqrt{3})=0$ ⇒ $(3\tan\theta−\sqrt{3})(\tan\theta−\sqrt{3})=0$ ⇒ $\tan\theta=\frac{1}{\sqrt{3}}$ or, $\tan\theta=\sqrt{3}$ ⇒ $\theta=30°$ or, $\theta=60°$ So, $\tan ^2 \theta+\cot ^2 \theta$ $=\tan^2 30° + \cot^2 30°$ $=\frac{1}{3}+3$ $=\frac{10}{3}$ Hence, the correct answer is $\frac{10}{3}$.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Question : If $\sec \theta+\tan \theta=\frac{1}{\sqrt{3}}$, then the positive value of $\cot \theta+\cos \theta$ is:
Question : If $\tan \theta \cdot \tan 2 \theta=1$, then the value of $\cot 5 \theta$ is:
Question : If $\tan (90-\theta)=\frac{2}{\sqrt{3}}$, then the value of $2 \sqrt{3} \tan \theta+1$ is:
Question : If $\sqrt{2} \sec ^2 \theta-4 \sec \theta+2 \sqrt{2}=0$, then what is the value $\sin ^2 \theta+\tan ^2 \theta$?
Question : If $6 \sec \theta=10$, then find the value of $\frac{5 \operatorname{cosec} \theta-3 \cot \theta}{4 \cos \theta+3 \sin \theta}$.
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile