Write the number of solutions of the equation 4 sin x – 3 cos x = 7.
4sin x – 3cos x = 7
4sin x – 7 = 3cos x
Squaring both sides
16(sin x)2 + 49 – 56sin x = 9(cos x)2
16(sin x)2 + 49 – 56sin x = 9((sin x)2-1)
16(sin x)2-9(sin x)2-56sin x+49+9=0
7(sin x)2-56sin x+58=0
Solving the quadratic equation
Sin x = 6.7774 or 1.2225
But we know that sinθ lies between [-1,1]
So there are no solutions for this given equation