# Ex 3.4, 7 - Chapter 3 Class 11 Trigonometric Functions

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Ex 3.4, 7 Find the general solution of the equation sin 2x + cos x = 0 sin 2x + cos x = 0 We know that sin 2x = 2 sin x cos x 2 sin x cos x + cos x = 0 cos x (2sin x + 1) = 0 Hence , cos x = 0 or 2sin x + 1 = 0 cos x = 0 or 2sin x = 0 1 cos x = 0 or 2sin x = 1 cos x = 0 or sin x = ( 1)/2 We find general solution of both equations separately General solution for cos x = 0 Let cos x = cos y Given cos x = 0 From (1) and (2) cos y = 0 cos y = cos /2 y = /2 General Solution is x = 2n y where n Z Putting y = /2 Hence, x = 2n /2 where n Z Finding general solution for sin x = ( )/ Let sin x = sin y given sin x = ( 1)/2 From (3) and (4) sin y = ( 1)/2 sin y = sin 7 /6 y = 7 /6 General Solution is x = n + ( -1 )n y where n Z Put y = 7 /6 Hence, x = n + (-1)n 7 /6 Where n Z Hence for cos x = 0, x = 2n /2 where n Z or for sin x = ( 1)/2 x = n + (-1)n 7 /6 Where n Z

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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.