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sum of integral values of n such that sin x(2sinx+cosx)=n, has at least one real solution is (a)0 (b)1 (c)2 (d)3

sum of integral values of n such that sin x(2sinx+cosx)=n, has at least one real solution is
(a)0  (b)1  (c)2 (d)3

Grade:12

1 Answers

Arun
25763 Points
4 years ago
2 sin^2x + 2sinx cosx/2 = n
sin2x+ 2(1-cos2x) = 2n
Sin2x - 2 cos2x = 2(n-1)
-\large \sqrt5 \large \sqrt5
1 -\large \sqrt5/2 \large \sqrt5/2
Hence integral values of n = 0, 1, 2
total number of integral value = 3 (option D)

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