Question : If $\sec A+\tan A=5$, then $\sin A$ is equal to:
Option 1: $\frac{5}{13}$
Option 2: $\frac{5}{12}$
Option 3: $\frac{13}{12}$
Option 4: $\frac{12}{13}$
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $\frac{12}{13}$
Solution : Given: $\sec A+\tan A=5$ ----------(equation 1) We know, $\sec^2A–\tan^2A=1$ ⇒ $(\sec A+\tan A)(\sec A–\tan A)=1$ ⇒ $5(\sec A–\tan A)=1$ ⇒ $\sec A–\tan A=\frac{1}{5}$ -----------(equation 2) Solving equations 1 and 2 we get, $\sec A=\frac{26}{10}$ and $\tan A=\frac{24}{10}$. So, $\sin A=\frac{\tan A}{\sec A}=\frac{\frac{24}{10}}{\frac{26}{10}}=\frac{12}{13}$. Hence, the correct answer is $\frac{12}{13}$.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : $\triangle \mathrm{ABC}$ is a right-angle triangle at $\mathrm{B}$. If $\tan \mathrm{A}=\frac{5}{12}$, then $\sin \mathrm{A}+\sin \mathrm{B}+\sin \mathrm{C}$ will be equal to:
Question : If $\sec A=\frac{5}{4}$, then the value of $\frac{\tan A}{1+\tan ^2 A}-\frac{\sin A}{\sec A}$ is:
Question : If $\sec\theta+\tan\theta=5$, then find the value of $\tan\theta$.
Question : If $\sec \ A + \tan \ A = 3$, then $\cos \ A$ is equal to:
Question : If $\tan A=\frac{5}{12}$, then the value of $\cos A=$______.
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile