1. Chapter 3 Class 11 Trigonometric Functions
2. Serial order wise
3. Ex 3.4

Transcript

Ex 3.4, 6 Find the general solution of the equation cos 3x + cos x โ cos 2x = 0 cos 3x + cos x โ cos 2x = 0 (cos 3x + cos x) โ cos 2x = 0 2 cos ((3๐ฅ + ๐ฅ)/2) . cos ((3๐ฅ โ ๐ฅ)/2) โ cos 2x = 0 2 cos (4๐ฅ/2) . cos (2๐ฅ/2) โ cos 2x = 0 2 cos (2x) . cos x โ cos 2x = 0 cos (2x) (2cos x โ 1) = 0 Hence cos 2x = 0 or (2cos x โ 1) = 0 cos 2x = 0 or 2cos x = 1 cos 2x = 0 or cos x = 1/2 We find general solutions of both separately General solution for cos 2x = 0 Let cos x = cos y โ cos 2x = cos 2y Given cos 2x = 0 From (1) and (2) cos 2y = 0 cos 2y = cos 90ยฐ cos 2y = cos ๐/2 2y = ๐/2 General solution for cos 2x = cos 2y is given by 2x = 2nฯ ยฑ 2y where n โ Z putting 2y = ๐/2 2x = 2nฯ ยฑ ๐/2 x = 1/2 (2nฯ ยฑ ๐/2) x = nฯ ยฑ ๐/2 General solution for cos x = ๐/๐ Let cos x = cos y Given cos x = 1/2 From (3) and (4) cos y = 1/2 cos (y) = cos (๐/3) โ y = ๐/3 General solution for cos x = cos y is x = 2nฯ ยฑ y where n โ Z putting y = ๐/3 x = nฯ ยฑ ๐/3 where n โ Z Hence General Solution is For cos 2x = 0, x = nฯ ยฑ ๐/2 & for cos x = 1/2 , x = nฯ ยฑ ๐/3 where n โ Z

Ex 3.4