Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide solution for RD Sharma maths class 12 chapter 5 Determinants exercise multiple choise question 34

Provide solution for RD Sharma maths class 12 chapter 5 Determinants exercise multiple choise question 34

Answers (1)

Answer:

Correct option (c)

Hint:

Solve the determinant by applying column operations.

Given:

Given that,

        \left|\begin{array}{lll} \sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x \end{array}\right|=0

We have to find the real root of the given determinant in interval

        [\frac{-\pi }{4},\frac{\pi }{4}]

Solution:

Here given that,

        \left|\begin{array}{lll} \sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x \end{array}\right|=0

Applying C1 → C1 - C2; C2 → C2 - C3

        \Rightarrow \quad\left|\begin{array}{ccc} \sin x-\cos x & 0 & \cos x \\ \cos x-\sin x & \sin x-\cos x & \cos x \\ 0 & \cos x-\sin x & \sin x \end{array}\right|=0

Taking common (sin x- cos x) from column 1 and 2 , we get

        \begin{aligned} &\quad(\sin x-\cos x)^{2}\left|\begin{array}{ccc} 1 & 0 & \cos x \\ -1 & 1 & \cos x \\ 0 & -1 & \sin x \end{array}\right|=0 \\ &\Rightarrow (\sin x-\cos x)^{2}(1(\sin x+\cos x)+\cos x(1))=0 \\ &\Rightarrow (\sin x-\cos x)^{2}(\sin x+2 \cos x)=0 \\ &\Rightarrow (\sin x-\cos x)^{2}=0 \text { or } \sin x+2 \cos x=0 \\ &\Rightarrow \, \sin x-\cos x=0 \text { or } \frac{\sin x}{\cos x}=-2 \\ &\Rightarrow \frac{\sin x}{\cos x}=1 \: \text \: or \tan x=-2 \\ &\Rightarrow \tan x=1 \text { or } \tan x=-2 \notin\left[\frac{-\pi}{4}, \frac{\pi}{4}\right] \end{aligned}

Since, \frac{-\pi }{4}\leq x\leq \frac{\pi }{4}

Hence tan x=1  is the required answer.

Posted by

Gurleen Kaur

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14
anam-khan

CBSE Board Exams 2025: Online portal for availing exemptions by CWSN students opens
anam-khan

Board Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO

Latest Question