InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
The sum of all the solutions in `[0, 4pi]` of the equation `tan x+ cot x+1= cos (x+pi/4)` isA. `3 pi`B. `pi//2`C. `7pi//2`D. `4pi` |
|
Answer» Correct Answer - C `tan x + cot x +1 = cos (x+pi/4)` or `tan x+cot x=cos(x+pi/4)-1` Now `tan x +cot x le-2` and `cos(x+pi/4)-1 ge -2` It implies that equality holds when both are `-2`. Thus, `cos(x+pi/4)=-1` `rArr x+pi/4=(2m+1)pi, m in Z` `rArr x=(3pi)/4` or `(11pi)/4` Therefore, the sum of the solutions is `(3pi)/4+(11pi)/4=(7pi)/2` |
|