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Trigonometry QA 6

Physics Helpline

L K Satapathy

Trigonometric Equation

cos cos 2 cos3 cos4 0x x x x

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Physics Helpline

L K Satapathy

Question : If 0 x 2 , then the number of real values of x , which satisfy the equation cos x + cos 2x + cos 3x + cos 4x = 0 , is

(a) 3 (b) 5 (c) 7 (d) 9

Answer :

(cos2 cos ) (cos4 cos3 ) 0x x x x

3 72cos cos 2cos cos 02 2 2 2x x x x

7 32cos cos cos 02 2 2x x x

52cos cos cos 02 2x x x

cos cos2 cos3 cos4 0x x x x

Trigonometry QA 6

52cos 0 , cos 0 cos 02 2x x or x

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L K Satapathy

( ) cos 0 (2 1)2 2 2x xii n

5 5( ) cos 0 (2 1)2 2 2x xiii n

3 3 7 9, , , , , ,2 2 5 5 5 5

Number of solutions = 7 [Ans]Correct option = (c)

3( ) cos 0 (2 1) , [0 2 ]2 2 2

i x x n x

Trigonometry QA 6

3 7 9(2 1) , , , , [0 2 ]5 5 5 5 5

x n x

All solutions of x in [0 x 2] are

(2 1) [0 2 ]x n x

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L K Satapathy

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