Question

find the possible value of sinx if 8sin - cosx = 4​

Answer 1

8 sin x – cos x = 4 [Given]

∴ 8 sin x – 4 = cos x ..... (i)

∴ sin2 x + cos2 x = 1

∴ sin2 x + (8 sin x – 4)2 = 1 [from (i)

∴ sin2 x + 64 sin2 x – 64 sin x + 16 = 1

∴ sin2 x + 64 sin2 x – 64 sin x + 16 – 1 = 0

∴ 65 sin2 x – 64 sin x + 15 = 0

∴ 65 sin2 x – 39 sin x – 25 sin x + 15 = 0

∴ 13 sin x (5 sin x – 3) – 5 (5 sin x – 3) = 0

∴ (5 sin x – 3) (13 sin x – 5) = 0

∴ 5 sin x – 3 = 0 or 13 sin x – 5 = 0

∴ 5 sin x = 3 or 13 sin x = 5

∴ sin x = 3/5 or sin x = 5/13

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