Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Ex 3.2
Ex 3.2, 2 (i)
Ex 3.2, 2 (ii) Important
Ex 3.2, 2 (iii)
Ex 3.2, 2 (iv)
Ex 3.2, 3 (i)
Ex 3.2, 3 (ii) Important
Ex 3.2, 3 (iii)
Ex 3.2, 3 (iv) Important
Ex 3.2, 3 (v)
Ex 3.2, 3 (vi) Important
Ex 3.2, 4
Ex 3.2, 5
Ex 3.2, 6
Ex 3.2, 7 (i)
Ex 3.2, 7 (ii) Important
Ex 3.2, 8
Ex 3.2, 9
Ex 3.2, 10
Ex 3.2, 11
Ex 3.2, 12 Important
Ex 3.2, 13 Important You are here
Ex 3.2, 14
Ex 3.2, 15
Ex 3.2, 16 Important
Ex 3.2, 17 Important
Ex 3.2, 18
Ex 3.2, 19 Important
Ex 3.2, 20 Important
Ex 3.2, 21 (MCQ) Important
Ex 3.2, 22 (MCQ) Important
Last updated at June 7, 2023 by Teachoo
Ex 3.2, 13 If F (x) = [β 8(cosβ‘π₯&γβsinγβ‘π₯&0@sinβ‘π₯&cosβ‘π₯&0@0&0&1)] , Show that F(x) F(y) = F(x + y) We need to show F(x) F(y) = F(x + y) Solving L.H.S. Given F(x) = [β 8(cosβ‘π₯&γβsinγβ‘π₯&0@sinβ‘π₯&cosβ‘π₯&0@0&0&1)] Finding F(y) Replacing x by y in F(x) F(y) = [β 8(πππβ‘π&γβπππγβ‘π&π@πππβ‘π&πππβ‘π&π@π&π&π)] Now, F(x) F(y) = [β 8(cosβ‘π₯&γβsinγβ‘π₯&0@sinβ‘π₯&cosβ‘π₯&0@0&0&1)] [β 8(cosβ‘π¦&γβsinγβ‘π¦&0@sinβ‘π¦&cosβ‘π¦&0@0&0&1)] = [β 8(cosβ‘π₯ cosβ‘π¦+(γβsinγβ‘π₯ ) sinβ‘γπ¦+0 γ &cosβ‘γπ₯(βsinβ‘γπ¦)+(βsinβ‘γπ₯)γcos yγβ‘γ+ 0γ γ γ γ&0+0+0Γ1@sinβ‘γπ₯ cosβ‘γπ¦+cosβ‘γπ₯ sinβ‘γπ¦+0γ γ γ γ&sinβ‘π₯ (βsinβ‘γπ¦)+γ cosβ‘γπ₯ cosβ‘γπ¦+0γ γ&0+0+0Γ1@0Γcosβ‘γπ¦ +0Γsinβ‘γπ¦+0Γ1γ γ&0Γ(βsinβ‘γπ¦)+0Γcosβ‘γπ¦+0γ γ&0+0+1Γ1)] = [β 8(cosβ‘π₯ cosβ‘π¦ γβsinγβ‘π₯.sinβ‘γπ¦ γ &γβcosγβ‘γπ₯ sinβ‘γπ¦βsinβ‘γπ₯ cosβ‘π¦ γ γ γ&0@sinβ‘γπ₯ cosβ‘γπ¦+cosβ‘γπ₯ sinβ‘π¦ γ γ γ&βsinβ‘π₯ sinβ‘γπ¦+γ cosβ‘γπ₯ cosβ‘π¦ γ&0@0&0&1)] = [β 8(cosβ‘γ(π₯+π¦)γ &γβ[cosγβ‘γπ₯ sinβ‘γπ¦+sinβ‘γπ₯ cosβ‘γπ¦]γ γ γ γ&0@sinβ‘γ(π₯+π¦)γ&cosβ‘π₯ cosβ‘γπ¦ βγ sinβ‘γπ₯ sinβ‘π¦ γ&0@0&0&1)] = [β 8(πππβ‘γ(π+π)γ &βπππβ‘γ(π+π)γ&π@πππβ‘γ(π+π)γ&πππβ‘γ(π+π)γ&π@π&π&π)] We know that cos x cos y β sin x sin y = cos (x + y) & sin x cos y + cos x sin y = sin (x + y) Solving R.H.S F(x + y) Replacing x by (x + y) in F(x) = [β 8(cosβ‘γ(π₯+π¦)γ &βsinβ‘γ(π₯+π¦)γ&0@sinβ‘γ(π₯+π¦)γ&cosβ‘γ(π₯+π¦)γ&0@0&0&1)] = L.H.S. Hence proved