Mathbee CBSE Mathbee · CBSE Class 12 Maths
Class 12 Determinants · Mcq Single Correct1 Marksmatrix_inverse

Class 12 Maths · Determinants · Mcq Single Correct #20

For cosθ≠0, let \(\begin{bmatrix}1 & -\tan\theta\\\tan\theta & 1\end{bmatrix}\)\(\begin{bmatrix}1 & \tan\theta\\-\tan\theta & 1\end{bmatrix}\)⁻¹=\(\begin{bmatrix}a & −b\\b & a\end{bmatrix}\). Find a,b.

✅ Step-by-Step Solution

Final Answer: Option (B): a=cos2θ,b=sin2θ
  1. With t=tanθ, the inverse of [[1,t],[−t,1]] is [[1,−t],[t,1]]/(1+t²). The product is [[1−t²,−2t],[2t,1−t²]]/(1+t²). Thus a=cos2θ and b=sin2θ.

Master Chapter 4: Determinants

Practise interactive questions, flashcards, visual mind maps, and timed board tests for Determinants.
📘 Chapter Notes & All Exercises 🚀 Open in Interactive Workspace →
← Previous Question
Vertices (a,b),(c,d),(e,f) form a triangle of area Δ. Find the…
Next Question →
Assertion: A determinant is a scalar associated with a square…

More Practice Questions in Determinants

Q1Q2Q3Q4Q5Q6Q7Q8Q9Q10Q11Q12Q13Q14Q15Q16Q17Q18Q19Q20Q21Q22Q23Q24Q25Q26Q27Q28Q29Q30Q31Q32Q33Q34Q35Q36Q37Q38Q39Q40

Related Questions in Determinants

Class 12 Determinants · Mcq Single Correct
If \(\begin{vmatrix}2 & 4\\5 & 1\end{vmatrix}\)=\(\begin{vmatrix}2x & 4\\6 &…
Class 12 Determinants · Mcq Single Correct
The area of the triangle with vertices (−3,0),(3,0),(0,k) is 9 square units. Find k.
Class 12 Determinants · Mcq Single Correct
Let f(x)=\(\begin{vmatrix}0 & x−a & x−b\\x+a & 0 & x−c\\x+b & x+c & 0\end{vmatrix}\). Which…
Class 12 Determinants · Mcq Single Correct
If \(\begin{vmatrix}2 & 3 & 2\\x & x & x\\4 & 9 & 1\end{vmatrix}\)+3=0, find x.
Class 12 Determinants · Mcq Single Correct
If x=−4 is a root of \(\begin{vmatrix}x & 2 & 3\\1 & x & 1\\3 & 2 & x\end{vmatrix}\)=0, find…
Class 12 Determinants · Mcq Single Correct
For a 3×3 real matrix A, det(Aᵀ)=−3. Find det(AAᵀ).