Question : Which of the following is equal to $\frac{1}{\tan \theta}+\tan \theta$?
Option 1: $\sec \theta \operatorname{cosec} \theta$
Option 2: $1$
Option 3: $\frac{\operatorname{cosec} \theta}{\sec \theta}$
Option 4: $\tan ^2 \theta$
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: $\sec \theta \operatorname{cosec} \theta$
Solution : Given: The trigonometric expression is $\frac{1}{\tan \theta}+\tan \theta$. We know the trigonometric identity $\sec^2\theta=1+\tan^2\theta$ ⇒ $\frac{1}{\tan \theta}+\tan \theta=\frac{1+\tan^2 \theta}{\tan \theta}$ $=\frac{\sec^2 \theta}{\tan \theta}=\frac{\sec^2 \theta}{\sin\theta}\times\cos\theta=\sec \theta \operatorname{cosec} \theta$ Hence, the correct answer is $\sec \theta \operatorname{cosec} \theta$.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : $\frac{(1+\tan \theta+\sec \theta)(1+\cot \theta-\operatorname{cosec} \theta)}{(\sec \theta+\tan \theta)(1-\sin \theta)}$ is equal to:
Question : Which of the following is equal to $[\frac{\cos \theta}{\sin \theta}+\frac{\sin \theta}{\cos \theta}]$?
Question : $\left(\frac{\tan ^3 \theta}{\sec ^2 \theta}+\frac{\cot ^3 \theta}{\operatorname{cosec}^2 \theta}+2 \sin \theta \cos \theta\right) \div\left(1+\operatorname{cosec}^2 \theta+\tan ^2 \theta\right), 0^{\circ}<\theta<90^{\circ}$, is equal to:
Question : The value of $\sqrt{\frac{1+\cos \theta}{1-\cos \theta}}$ is:
Question : For any real values of $\theta, \sqrt{\frac{\sec\theta \:-\: 1}{\sec\theta \:+\: 1}}=$?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile