Question

If sin x = -cos x, x is greater than 0 and less than 2pi find the possible values of x.

Answer 1

Dear student
$$\begin{gathered} \mathrm{sinx}+\mathrm{cosx}=0 \\ \Rightarrow \frac{\mathrm{sinx}+\mathrm{cosx}}{\mathrm{cosx}}=\frac{0}{\mathrm{cosx}} \\ \Rightarrow \mathrm{tanx}+1=0 \\ \Rightarrow \mathrm{tanx}=-1 \\ \Rightarrow \mathrm{x}=\frac{3\mathrm{\pi }}{4}+\mathrm{\pi n} \end{gathered}$$
Regards