Question : If $\sin\theta+\cos\theta=\sqrt{2}\cos\theta$, then the value of $\cot\theta$ is:
Option 1: $\sqrt{2}+1$
Option 2: $\sqrt{2}-1$
Option 3: $\sqrt{3}-1$
Option 4: $\sqrt{3}+1$
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: $\sqrt{2}+1$
Solution : $\sin\theta+\cos\theta=\sqrt{2}\cos\theta$ ⇒ $\sin \theta = (\sqrt{2}-1)\cos\theta$ ⇒ $\frac{\sin \theta}{(\sqrt{2}-1)}=\cos\theta$ ⇒ $\frac{\sin \theta(\sqrt{2}+1)}{2-1}=\cos\theta$ ⇒ $\frac{\sin \theta(\sqrt{2}+1)}{2-1}=\cos\theta$ ⇒ $\frac{\cos \theta}{\sin \theta}=\sqrt{2}+1$ $\therefore\cot \theta=\sqrt{2}+1$ Hence, the correct answer is $\sqrt{2}+1$.
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 $(4 \sin \theta+5 \cos \theta)=3$, then the value of $(4 \cos \theta-5 \sin \theta)$ is:
Question : If $\theta$ is an acute angle and $\sin \theta \cos \theta=2 \cos ^3 \theta-\frac{1}{4} \cos \theta$, then the value of $\sin \theta$ is:
Question : The value of $\frac{\sin\theta-2\sin^{3}\theta}{2\cos^{3}\theta-\cos\theta}$ is equal to:
Question : If $(\sin \theta-\cos \theta)=0$, then the value of $\sin\;(\pi-\theta)+\sin \left(\frac{\pi}{2}-\theta\right)$ is:
Question : If $\sin \theta \cos \theta=\frac{1}{\sqrt{3}}$ then the value of $\left(\sin ^4 \theta+\cos ^4 \theta\right)$ is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile