Q2 of 142 Page 11

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


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