Question : If $\sec \theta+\tan \theta=\frac{1}{\sqrt{3}}$, then the positive value of $\cot \theta+\cos \theta$ is:
Option 1: $\frac{3 \sqrt{3}}{2}$
Option 2: $\frac{\sqrt{3}}{2}$
Option 3: $\frac{2}{3 \sqrt{3}}$
Option 4: $\frac{2}{\sqrt{3}}$
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: $\frac{3 \sqrt{3}}{2}$
Solution : Given: $\sec \theta+\tan \theta=\frac{1}{\sqrt{3}}$...................(equation 1) We know that $\sec^2\theta-\tan^2\theta=1$ $⇒(\sec\theta-\tan\theta)(\sec\theta+\tan\theta)=1$ Putting the value, we get $⇒(\sec\theta-\tan\theta)(\frac{1}{\sqrt3})=1$ $⇒(\sec\theta-\tan\theta)=\sqrt3$............(equation 2) From equations 1 and 2, we get: $⇒2\sec\theta=\sqrt3+\frac{1}{\sqrt3}$ $⇒2\sec\theta=\frac{4}{\sqrt3}$ $⇒\sec\theta=\frac{2}{\sqrt3}$ We know that, $\sec\theta=\frac{h}{b}=\frac{2}{\sqrt3}$ So, $p=\sqrt{ h^2-b^2}$ $⇒p=\sqrt{2^2-\sqrt3^2}=1$ $\therefore \cot\theta+\cos\theta=\frac{b}{p}+\frac{b}{h}=\frac{\sqrt3}{1}+\frac{\sqrt3}{2}=\frac{3\sqrt3}{2}$ Hence, the correct answer is $\frac{3\sqrt3}{2}$.
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 $\cos \theta+\sec \theta=\sqrt{3}$, then the value of $\cos ^3 \theta+\sec ^3 \theta$ is:
Question : If $\sqrt{3} \tan ^2 \theta-4 \tan \theta+\sqrt{3}=0$, then what is the value of $\tan ^2 \theta+\cot ^2 \theta$?
Question : If $(r\cos \theta -\sqrt{3})^{2}+(r\sin \theta -1)^{2}=0$, then the value of $\frac{r\tan \theta +\sec \theta}{r\sec \theta +\tan\theta}$ is equal to:
Question : If $\theta$ is a positive acute angle and $4\cos ^{2}\theta -4\cos \theta +1=0$, then the value of $\tan (\theta -15^{\circ})$is equal to:
Question : If $\sin\theta+\cos\theta=\sqrt{2}\cos\theta$, then the value of $\cot\theta$ is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile