Let M=[\table \sin^4\theta,-1-\sin^2\theta;1+\cos^2\theta,\cos^4\theta]=\alphaI+\betaM^{-1} Where \alpha=\alpha(\theta) and \beta=\beta(\theta) are real numbers, and I is the 2\times2 identity matrix. If \alpha* is the minimum of the set \{\alpha(\theta):\theta\in[0,\pi)\} and β* is the minimum of the set \{\beta(\theta):\theta\in[0,2\pi)\}.Then the value of \alpha*+\beta* is [JEE Adv 2019 P1]

Matrices and Determinants

Section: Mathematics

Question : 22 of 56

Marks: +1, -0

Let

M=[

sin4θ	−1−sin2θ
1+cos2θ	cos4θ

]=αI+βM−1

Where α=α(θ) and β=β(θ) are real numbers, and I is the 2×2 identity matrix. If
α* is the minimum of the set {α(θ):θ∈[0,π)} and
β* is the minimum of the set {β(θ):θ∈[0,2π)}.Then the value of α*+β* is

[JEE Adv 2019 P1]

−
29
16
−
37
16
−
31
16
−
17
16

Validate

Go to Question:

Prev Question

Next Question

cos4θ	1+sin2θ
−1−cos2θ	sin4θ