Question : If $\operatorname{cosec B} = \frac{3}{2}$, then what is the value of $\mathrm{\cot B \sin B} $?
Option 1: $\frac{\sqrt{5}}{3}$
Option 2: $\frac{4}{3 \sqrt{3}}$
Option 3: $\frac{3 \sqrt{2}}{2}$
Option 4: $\frac{2 \sqrt{5}}{3}$
New: SSC CHSL Tier 2 answer key released | 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: $\frac{\sqrt{5}}{3}$
Solution : Given that $\operatorname{cosec B} = \frac{3}{2}$. $\mathrm{\sin B = \frac{2}{3}}$ $⇒\mathrm{\cos B = \sqrt{1 - \sin^2 B} = \sqrt{1 - \left(\frac{2}{3}\right)^2} = \sqrt{1 - \frac{4}{9}} = \sqrt{\frac{5}{9}} = \frac{\sqrt{5}}{3}}$ $⇒\mathrm{\cot B = \frac{\cos B}{\sin B} = \frac{\frac{\sqrt{5}}{3}}{\frac{2}{3}} = \frac{\sqrt{5}}{2}}$ $\therefore \mathrm{\cot B \sin B = \frac{\sqrt{5}}{2} \times \frac{2}{3} = \frac{\sqrt{5}}{3}}$ Hence, the correct answer is $\frac{\sqrt{5}}{3}$.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Question : Simplify the given equation: $\frac{\cot^3A–1}{\cot A–1}$
Question : If $\theta$ is a positive acute angles and $\operatorname{cosec}\theta =\sqrt{3}$, then the value of $\cot \theta -\operatorname{cosec}\theta$ is:
Question : What is the value of $\frac{\cot \theta+\operatorname{cosec} \theta-1}{\cot \theta-\operatorname{cosec} \theta+1}$?
Question : What is the value of the expression: $\sin A(1+\frac{\sin A}{\cos A})+\cos A(1+\frac{\cos A}{\sin A})$?
Question : If $-\sin \theta+\operatorname{cosec} \theta=6$, then what is the value of $\sin \theta+\operatorname{cosec} \theta$ ?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile