Solve the equation cos 5 cos 7 0 on the interval 0 2Solutio

Solve the equation cos 5 cos 7 = 0 on the interval [0, 2)

Solution

cos 5x-cos7x= 0 [As cos A cos B = 2 sin (A + B)2 * sin (A B)/2 ]

2 sin 6x sin x = 0

sin 6x sin x = 0

sin 6x = 0 when 6x = (+/-) n (pi) ========> x = (+/-) [n (pi)]/6

sin x = 0 when x = (+/-) n (pi)

x = (+/-) [n(pi)]/6 [ -(pi), (pi)] this answer is true for this intervals in which n is between the numbers 6

and negative 6 the exact values are : (+/-) [1(pi)]/6 (+/-) [2(pi)]/6 and so forth till you reach 6