Question : If $\sin \theta-\cos \theta=\frac{1}{5}$, then find the value of $\sin \theta+\cos \theta$.
Option 1: $\frac{5}{7}$
Option 2: $\frac{7}{5}$
Option 3: $\frac{5}{3}$
Option 4: $\frac{3}{5}$
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: $\frac{7}{5}$
Solution : Given, $\sin \theta-\cos \theta=\frac{1}{5}$ Squaring both sides, we get, $\sin^2 \theta+\cos^2 \theta -2\sin \theta \cos \theta=\frac{1}{25}$ $⇒1-2\sin \theta \cos \theta=\frac{1}{25}$ $⇒2\sin \theta \cos \theta=\frac{24}{25}$ Adding 1 with both sides, we get, $⇒\sin^2 \theta+\cos^2 \theta +2\sin \theta \cos \theta=1+\frac{24}{25}$ [$\because \sin^2 \theta+\cos^2 \theta=1$] $⇒(\sin \theta+\cos \theta)^2=\frac{49}{25}$ $⇒\sin \theta+\cos \theta = \frac{7}{5}$ Hence, the correct answer is $\frac{7}{5}$.
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 $\frac{\sin\theta+\cos\theta}{\sin\theta-\cos\theta}=3$, then the value of $\sin^{4}\theta$ is:
Question : If $\sin \theta+\cos \theta=\frac{1}{29}$, then find the value of $\frac{\operatorname{sin} \theta+\operatorname{cos} \theta}{\operatorname{sin} \theta-\operatorname{cos} \theta}$.
Question : If $\sin \theta \cos \theta=\frac{1}{\sqrt{3}}$ then the value of $\left(\sin ^4 \theta+\cos ^4 \theta\right)$ is:
Question : If $\sin \theta \cos \theta=\frac{\sqrt{2}}{3}$,then the value of $\left(\sin ^6 \theta+\cos ^6 \theta\right)$ is:
Question : If $6 \cot \theta=5$, then find the value of $\frac{(6 \cos \theta+\sin \theta)}{(6 \cos\theta-4 \sin\theta)}$
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile