Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Find the range of function  <img alt="\tan \frac{\alpha}{2} \cdot \tan \alpha" src="https://learn.careers360.com/latex-image/?%5Ctan%20%5Cfrac%7B%5Calpha%7D%7B2%7D%20%5Ccdot%20%5Ctan%20%5

Find the range of function  \tan \frac{\alpha}{2} \cdot \tan \alpha

Option: 1

(-\infty,-2] U[0,\infty)


Option: 2

(-\infty,\infty)


Option: 3

(-\infty,-1] U[1,\infty)


Option: 4

(-\infty,-1] U[0,\infty)


Answers (1)

best_answer

Half Angle Formula -

Half Angle Formula

 

 

\begin{aligned}1.\;\;\; \sin \left(\frac{\alpha}{2}\right) &=\pm \sqrt{\frac{1-\cos \alpha}{2}} \\ 2.\;\;\;\cos \left(\frac{\alpha}{2}\right) &=\pm \sqrt{\frac{1+\cos \alpha}{2}} \\3.\;\;\; \tan \left(\frac{\alpha}{2}\right) &=\pm \sqrt{\frac{1-\cos \alpha}{1+\cos \alpha}} =\frac{\sin \alpha}{1+\cos \alpha}=\frac{1-\cos \alpha}{\sin \alpha} \end{aligned}

 

-

\tan \frac{\alpha}{2} \cdot \tan \alpha=(\frac{1-\cos \alpha}{\sin \alpha}) \cdot \frac{\sin \alpha}{\cos \alpha}\\ =\sec \alpha -1\\ \text{ Range of sec } \alpha (-\infty,-1] U[1,\infty)\\ \text{ Range of } f(\alpha) is (-\infty,-2] U[0,\infty)\\

Posted by

Riya

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Mains 2026 City Intimation LIVE: NTA to issue session 1 city slip soon; exam timings, guidelines
anam-khan

JEE Main 2026: Experts share final-week strategy for subject-wise revision, mock tests
anam-khan

JEE Main 2026 City Intimation Slip Date LIVE: NTA to issue exam city slip, admit card soon; test date,syllabus

Latest Question