Question

Write the number of solutions of the equation 4 sin x-3 cos x =7.

Answer 1

$4sinx-3cosx=7\text{Divede both sides by}\sqrt{3^2+4^2}=5\frac{4}{5}sinx-\frac{3}{5}cosx=\frac{7}{5}sin(x-ta{n}^{-}1\left(\frac{3}{4}\right))=1.4\text{We know that range of sine function is[-1,1]}\Rightarrow sin(x-ta{n}^{-1}\left(\frac{3}{4}\right))\ne 1.4\text{so number of solutions in Zero.}$