Ask Questions, Get Answers

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

Number of solutions of the equation $\tan x+\sec x=2\cos x$ lying in the interval $[0,2\pi]$ is

$\begin{array}{1 1}(A)\;0&(B)\;1\\(C)\;2&(D)\;3\end{array} $

Can you answer this question?

1 Answer

0 votes
Given :
$\tan x+\sec x =2\cos x$
$\large\frac{\sin x}{\cos x}+\frac{1}{\cos x}$$=2\cos x$
$(\sin x+1)=2\cos^2x$
$\sin x+1=2-2\sin^2x$
$2\sin^2x+\sin x-1=0$
$2\sin^2x+2\sin x-\sin x-1=0$
$2\sin x(\sin x+1)-1(\sin x+1)=0$
$(2\sin x-1)(\sin x+1)=0$
If $2\sin x-1=0$
$\sin x=\large\frac{1}{2}$
If $\sin x+1=0$
$\sin x=-1$
Hence (C) is the correct option.
answered Apr 21, 2014 by sreemathi.v

Related questions

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