Question : What is the value of $\frac{1+\tan A}{\operatorname{cosec} A}+\frac{1+\cot A}{\sec A}$?
Option 1: $2\sec^2A$
Option 2: $\sec \mathrm{A} - \mathrm{cosec A}$
Option 3: $\sec \mathrm{A} + \mathrm{cosec A}$
Option 4: $2 \;\mathrm{cosec^2 A}$
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: $\sec \mathrm{A} + \mathrm{cosec A}$
Solution : $\frac{1+\tan A}{\operatorname{cosec} A}+\frac{1+\cot A}{\sec A}$ $=\frac{1+\frac{\sin A}{\cos A}}{\frac{1}{\sin A}}+\frac{1+\frac{\cos A}{\sin A}}{\frac{1}{\cos A}}$ $=\sin A(1+\frac{\sin A}{\cos A})+\cos A(1+\frac{\cos A}{\sin A})$ $=\sin A(\frac{\cos A+\sin A}{\cos A})+\cos A(\frac{\cos A+\sin A}{\sin A})$ $=(\sin A+\cos A)(\frac{\sin A}{\cos A}+\frac {\cos A}{\sin A}))$ $=(\sin A+\cos A)(\frac{\sin ^2A+\cos^2A}{\sin A \cos A}))$ $=(\frac{\sin A+\cos A}{\sin A \cos A})$ [$\because \left ( \sin ^2A+\cos^2A=1 \right )$] $=(\frac{\sin A}{\sin A \cos A})+(\frac{\cos A}{\sin A \cos A})$ $=(\frac{1}{ \cos A})+(\frac{1}{\sin A})$ $=\sec \mathrm{A} + \mathrm{cosec A}$ Hence, the correct answer is $\sec \mathrm{A} + \mathrm{cosec A}$.
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 : What is the value of $\frac{\cot \theta+\operatorname{cosec} \theta-1}{\cot \theta-\operatorname{cosec} \theta+1}$?
Question : What is the value of $\sqrt{\frac{\operatorname{cosec} A+1}{\operatorname{cosec} A-1}}+\sqrt{\frac{\operatorname{cosec} A-1}{\operatorname{cosec} A+1}}$?
Question : The given expression is equal to: $\frac{\left(1+\tan^2 A\right)}{\operatorname{cosec}^2 A \cdot \tan A}$
Question : What is the value of the expression: $\sin A(1+\frac{\sin A}{\cos A})+\cos A(1+\frac{\cos A}{\sin A})$?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile