Question : If $\sin \theta+\cos \theta = p$ and $\sec \theta + \operatorname{cosec} \theta = q$, then the value of $q \times (p^2-1)$ is:
Option 1: $1$
Option 2: $p$
Option 3: $2p$
Option 4: $2$
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: $2p$
Solution : Given: $\sin \theta+\cos \theta = p$ and $\sec \theta + \operatorname{cosec} \theta = q$ Now, $q \times (p^2-1)$ Putting the values, we get: = $(\sec \theta + \operatorname{cosec} \theta) [(\sin \theta+\cos \theta)^2 - 1]$ = $(\frac{1}{\cos \theta} + \frac{1}{\sin \theta})(2 \sin \theta \cos\theta)$ = $(\frac{\sin\theta + \cos\theta}{\sin \theta \cos\theta})(2 \sin \theta \cos\theta)$ = $2(\sin \theta +\cos\theta)$ = $2p$ Hence, the correct answer is $2p$.
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 $\cos \theta+\sin \theta=\sqrt{2}$, then what is the value of $\sec \theta \operatorname{cosec} \theta$ ?
Question : The value of $\frac{1+\sin A}{\cos A}+\frac{\cos A}{1+\sin A}$ is:
Question : If $\frac{\sin \theta-\cos \theta}{\sin \theta+\cos \theta}=\frac{4}{5}$, then the value of $\frac{\operatorname{cosec}^2 \theta}{2-\operatorname{cosec}^2 \theta}$ is:
Question : What is the value of $\frac{\cot \theta+\operatorname{cosec} \theta-1}{\cot \theta-\operatorname{cosec} \theta+1}$?
Question : If $\sin \theta+\cos \theta=\frac{1}{29}$, then find the value of $\frac{\operatorname{sin} \theta+\operatorname{cos} \theta}{\operatorname{sin} \theta-\operatorname{cos} \theta}$.
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile