Question

solve the trigonometric equation i) 4cos(theta) -3 cos(theta) - tan(theta)

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{given}\mathrm{trigonometric}\mathrm{function}\mathrm{is}, \\ =4\mathrm{cos\theta }-3\mathrm{cos\theta }-\mathrm{tan\theta } \\ =\mathrm{cos\theta }-\mathrm{tan\theta } \\ =\mathrm{cos\theta }-\frac{\mathrm{sin\theta }}{\mathrm{cos\theta }} \\ =\frac{{\cos }^2\mathrm{\theta }-\mathrm{sin\theta }}{\mathrm{cos\theta }} \\ =\frac{1-{\sin }^2\mathrm{\theta }-\mathrm{sin\theta }}{\mathrm{cos\theta }} \\ \mathrm{It}\mathrm{cannot}\mathrm{be}\mathrm{further}\mathrm{reduced}. \end{gathered}$$