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Last updated at Jan. 23, 2020 by Teachoo

Transcript

Misc 15 Using properties of determinants, prove that: |■8(sinα&cosα&cos〖(α+δ)〗@sinβ&cosβ&cos〖(β+δ)〗@sinγ&cosγ&cos〖(γ+δ)〗 )| = 0 Let ∆ = |■8(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 = |■8(sinα&cosα&cos𝛼 cos〖δ −sin〖𝛼 sin𝛿 〗 〗@sinβ&cosβ&cos𝛽 cos〖𝛿−sin〖𝛽 sin𝛿 〗 〗@sinγ&cosγ&cosγcos 𝛿 −sin〖γ sin𝛿 〗 )| Expressing elements of 2nd row as sum of two elements = |■8(sinα&cosα&cos 𝛼 cos〖δ 〗@sinβ&cosβ&cos𝛽 cos𝛿@sinγ&cosγ&cos γ cos 𝛿 )| + |■8(sinα&cosα&−sin〖𝛼 sin𝛿 〗@sinβ&cosβ&−sin〖𝛽 sin𝛿 〗@sinγ&cosγ&−sin〖γ sin𝛿 〗 )| 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. Taking cos 𝛿 common from C3 = cos〖δ 〗 |■8(sinα&cosα&cos 𝛼@sinβ&cosβ&cos𝛽@sinγ&cosγ&cos γ )| + (−sin𝛿) |■8(sinα&cosα&sin𝛼@sinβ&cosβ&sin𝛽@sinγ&cosγ&sinγ )| = cos〖δ 〗(0) + (−sinδ) (0) = 0 = R.H.S Hence proved Using Property: If any two row or column are identical, then value of determinant is zero

Miscellaneous

Misc 1

Misc. 2 Important

Misc 3

Misc 4

Misc 5

Misc 6 Important

Misc 7 Important

Misc 8

Misc 9

Misc 10

Misc 11 Important

Misc 12 Important

Misc. 13

Misc 14

Misc. 15 Important You are here

Misc. 16 Important

Misc 17 Important

Misc 18

Misc 19 Important

Matrices and Determinants - Formula Sheet and Summary

Chapter 4 Class 12 Determinants

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.