Question

if 8sinx - cosx= 4 find values of sinx​

Answer 1

Answer:

Step-by-step explanation:

8sin x - cos x = 4

Therefore,

8sin x - 4 = cos x

We Know,

sin^2 x + cos^2 x = 1…(Trigonometric Identity)

Thus,

sin^2 x + (8sin x - 4)^2 = 1

sin^2 x + 64 sin^2 x -64 sinx + 16 = 1

…(Since (a + b)^2 = a^2 + 2ab + b^2)

Therefore,

65sin^2 x - 64 sin x + 16 = 1

65sin^2x - 64 sin x + 15 = 0

Solving this quadratic equation, we get,

sin x = 3/5 and sin x = 5/13

Thus, possible values of sin x are:

sin x = { 3/5 , 5/13}