Question

Find the determinant of matrix sin20.-cos20.Sin70.Cos70

Answer 1

Answer:

The determinant of matrix will be 1

Step-by-step explanation:

The given matrix component can be written as,

A₁₁ = sin20

A₁₂ = -cos20

A₂₁ = sin70

A₂₂ = cos70

The determinant of the matrix is given by,

|A| = A₁₁A₂₂ - A₁₂A₂₁

= sin20.cos70 - (-cos20.sin70)

= sin20.cos70 + cos20.sin70

we know that sin(A+B) can be written as

sin(A+B) = sinAcosB + sinBcosA

hence,

|A| = sin20.cos70 + cos20.sin70 = sin(20 + 70)

=> |A| = sin 90 = 1

Hence the determinant of matrix will be 1