Question

Find the number of integral values of a for which the equation cos 2x + a sin x = 2a - 7 possesses a
solution.​

Answer 1

Answer:

{ -6, -5 ,-4, ,-3, -2 }

Step-by-step explanation:

cos 2x + a sin x = 2a - 7

[ 1 - 2sin^2(x) ] + a sin x = 2a - 7

2sin^2(x) - a sin x - (2a + 8 ) = 0 ( quadratic eq )

sin x = [ a ± √(a^2 + 8 ( 2a + 8 ) ] / 4

sin x = [ a ± √(a^2 + 64 + 16a) ] / 4

sin x = [ a ± (a + 8 ) ] / 4

sin x = -2 or sin x = (a + 4) /2

since sin ≠ -2 and -1 ≤ sin x ≤ +1

-1 ≤ (a + 4) /2 ≤ +1

-2 ≤ (a + 4) ≤ +2

-6 ≤ a ≤ -2

hence.....

a = { -6, -5 ,-4, ,-3, -2 }