Question

Solve the trigonometric equations:
(i) cos²x + 3sin²​x = 0
(ii) cosx - cos2x + cosx - cos4x = 0

Answer 1

Dear student
$$\begin{gathered} 1){\cos }^2\mathrm{x}+3{\sin }^2\mathrm{x}=0 \\ \Rightarrow {\cos }^2\mathrm{x}+{\sin }^2\mathrm{x}+2{\sin }^2\mathrm{x}=0 \\ \Rightarrow 1+2{\sin }^2\mathrm{x}=0\left[\because {\sin }^2\mathrm{x}+{\cos }^2\mathrm{x}=1\right] \\ \Rightarrow 2{\sin }^2\mathrm{x}=-1 \\ \Rightarrow {\sin }^2\mathrm{x}=\frac{-1}{2} \\ \Rightarrow \mathrm{sinx}=\sqrt{\frac{-1}{2}} \end{gathered}$$
For remaining queries we request you to post them in separate threads to have rapid assistance from our experts.

Regards