
Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Ex 3.3
Ex 3.3, 2
Ex 3.3, 3
Ex 3.3, 4 Important
Ex 3.3, 5 (i)
Ex 3.3, 5 (ii)
Ex 3.3, 6 (i)
Ex 3.3, 6 (ii) Important You are here
Ex 3.3, 7 (i)
Ex 3.3, 7 (ii) Important
Ex 3.3, 8
Ex 3.3, 9
Ex 3.3, 10 (i) Important
Ex 3.3, 10 (ii)
Ex 3.3, 10 (iii) Important
Ex 3.3, 10 (iv)
Ex 3.3, 11 (MCQ) Important
Ex 3.3, 12 (MCQ)
Last updated at June 8, 2023 by Teachoo
Ex 3.3, 6 (ii) If A = [■8(sin𝛼&cos𝛼@−cos𝛼&sin𝛼 )] , then verify that A’ A = I Solving L.H.S A’ A Given A = [■8(sin𝛼&cos𝛼@−cos𝛼&sin𝛼 )] So, A’ = [■8(sin𝛼&〖−cos〗𝛼@cos𝛼&sin𝛼 )] A’ A = [■8(sin𝛼&〖−cos〗𝛼@cos𝛼&sin𝛼 )] [■8(sin𝛼&cos𝛼@〖−cos〗𝛼&sin𝛼 )] = [■8(sin𝛼 〖.sin〗𝛼+〖(−cos〗〖𝛼)〖(−cos〗〖𝛼)〗 〗&sin𝛼 〖.cos〗𝛼+〖(−cos〗〖𝛼)〖(sin〗〖𝛼)〗 〗@cos𝛼 〖.sin〗𝛼+sin〖𝛼 〖(−cos〗〖𝛼)〗 〗&cos𝛼 〖.cos〗𝛼+sin〖𝛼 〖.sin〗𝛼 〗 )] = [■8(sin2𝛼+cos2𝛼&sin〖𝛼 cos〖𝛼−cos〖𝛼 sin𝛼 〗 〗 〗@cos𝛼 sin〖𝛼−sin𝛼 〗 cos𝛼&cos2𝛼+sin2𝛼)] = [■8(𝐬𝐢𝐧𝟐𝜶+𝐜𝐨𝐬𝟐𝜶&𝟎@𝟎&𝐜𝐨𝐬𝟐𝜶+𝐬𝐢𝐧𝟐𝜶)] Using sin2 θ + cos2 θ = 1 = [■8(1&0@0&1)] = I = R.H.S Hence L.H.S = R.H.S Hence Proved