Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain solution RD Sharma class 12 chapter Determinants exercise multiple choise question 20 maths

Explain solution RD Sharma class 12 chapter Determinants exercise multiple choise question 20 maths

Answers (1)

Answer:

Correct option (b)

Hint:

Simply first solve the determinant.

Given:

Here the distinct real roots of

        \left|\begin{array}{ccc} \cos e c x & \sec x & \sec x \\ \sec x & cos\, ecx & \sec x \\ \sec x & \sec x & \cos e c x \end{array}\right|=0

lies in the interval

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

We have to find the number of roots of the given determinant.

Solution:

        Here\; \; \left|\begin{array}{ccc} \cos e c x & \sec x & \sec x \\ \sec x & cos\, ecx & \sec x \\ \sec x & \sec x & \cos e c x \end{array}\right|=0

Applying C1→C1-C3; C2→C2-C3

Taking common cos sec x-sec sec x  from column 1 and 2, we get

        \Rightarrow(cos\, \, ecx-\sec x)^{2}\left|\begin{array}{ccc} 1 & 0 & \sec x \\ 0 & 1 & \sec x \\ -1 & -1 & \cos e c x \end{array}\right|=0

Expanding along R1 , we get

          \Rightarrow(cos\, \, ecx-\sec x)^{2}[(cos\, ecx+sec\, x)+sec\, x(0+1)]=0

        \Rightarrow(cos\, \, ecx-\sec x)^{2}(cos\, ecx+2sec\, x)=0

        \Rightarrow(cos\, \, ecx-\sec x)^{2}=0\; \; or\; \; (cos\, ecx+2sec\, x)=0

        \Rightarrow cos\, \, ecx-\sec x =0\; \; or\; \; cos\, ecx=-2sec\, x

        \Rightarrow cos\, \,cos\, x-sin sin\, x =0\; \; or\; \; cos \, cos\, x=-2sin\, sin\, x

        \Rightarrow sin\, x =cos\, x\; \; or\; \;\frac{cos\, cos\, x}{sin\, sin\, x}=-2

        \Rightarrow \frac{cos\, cos\, x}{sin\, sin\, x}=1\; \;or\, \, cot\, cot\, x=-2

        \Rightarrow cot\, cot\, x=1\; \;or\, \, cot\, cot\, x=-2

        \Rightarrow tan\, tan\, x=1\; \;or\, \, tan\, tan\, x=-\frac{1}{2}

Hence, there are two solutions.

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

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years

Latest Question