logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  CBSE XI  >>  Math  >>  Trigonometric Functions
0 votes

If $\cot\theta+\tan\theta=2cosec \theta$,then find the general value of $\theta$

$\begin{array}{1 1}(A)\;2n\pi\pm \large\frac{\pi}{3}&(B)\;n\pi\pm \large\frac{\pi}{4}\\(C)\;3n\pi\pm \large\frac{\pi}{5}&(D)\;2n\pi\pm \large\frac{\pi}{8}\end{array} $

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • $\sin^2\theta+\cos^2\theta=1$
  • $\tan\theta=\large\frac{\sin \theta}{\cos \theta}$
  • $\cot \theta=\large\frac{\cos \theta}{\sin \theta}$
$\cot\theta+\tan\theta=2cosec \theta$
$\large\frac{\cos \theta}{\sin \theta}+\large\frac{\sin \theta}{\cos \theta}$$=\large\frac{2}{\sin \theta}$
$\large\frac{\cos^2\theta+\sin^2\theta}{\sin \theta\cos\theta}=\frac{2}{\sin \theta}$
$\large\frac{1}{\cos\theta}$$=2$
$\cos\theta=\large\frac{1}{2}$
Principal value =$\large\frac{\pi}{3},\frac{5\pi}{3}$
$\therefore$ General value $2n\pi\pm \large\frac{\pi}{3}$
Hence (A) is the correct answer.
answered Apr 18, 2014 by sreemathi.v
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...