# Misc. 15 - Chapter 4 Class 12 Determinants

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Misc. 15 Using properties of determinants, prove that: sinα cosα cos(α+δ) sinβ cosβ cos(β+δ) sinγ cosγ cos(γ+δ) = 0 Let ∆ = sinα cosα cos(α+δ) sinβ cosβ cos(β+δ) sinγ cosγ cos(γ+δ) Using cos (x + y) = cos x cos y – sin x sin y = sinα cosαcos𝛼 cosδ − sin𝛼 sin𝛿 sinβ cosβ cos𝛽 cos𝛿− sin𝛽 sin𝛿 sinγ cosγcosγcos 𝛿 − sinγ sin𝛿 Expressing elements of 2nd row as sum of two elements Using Property : If some or all elements of a row or column of a determinant are expressed as sum of two (or more) terms ,then the determinant is expressed as a sum of two (or more) determinants. = sinα cosαcos 𝛼 cosδ sinβ cosβ cos𝛽 cos𝛿 sinγ cosγcos γ cos 𝛿 + sinα cosα− sin𝛼 sin𝛿 sinβ cosβ− sin𝛽 sin𝛿 sinγ cosγ− sinγ sin𝛿 = cosδ sinα cosαcos 𝛼 sinβ cosβ cos𝛽 sinγ cosγcos γ + (− sin𝛿) sinα cosα sin𝛼 sinβ cosβ sin𝛽 sinγ cosγ sinγ = cosδ (0) + (− sinδ) (0) = 0 = R.H.S Hence proved

Chapter 4 Class 12 Determinants

Serial order wise

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.