Question

Let 

M= [(sin⁴θ  ,- 1-sin²θ)(1+cos²θ  , cos⁴θ)] =lα+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, 2π)} and β* is the minimum of the set {β(θ) : θ ∈ [0, 2π)}, then the value of α* + β* is

(A) -17/ 16 

(B) -29/16 

(C) - 31 /16 

(D) -37/16

Answer 1

Correct Option :-  -29 /16

Explanation :-