Question

Value of theta

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$when\frac{\cos \theta -\sin \theta }{\cos \theta +\sin \theta }=\frac{1-\sqrt{3}}{1+\sqrt{3}}$

Answer 1

$$\begin{gathered} \mathrm{Hi}, \\ \frac{\mathrm{cos\theta }-\mathrm{sin\theta }}{\mathrm{cos\theta }+\mathrm{sin\theta }}=\frac{1-\sqrt{3}}{1+\sqrt{3}} \\ \mathrm{Divide}\mathrm{by}\mathrm{cos\theta }\mathrm{in}\mathrm{LHS},\mathrm{both}\mathrm{in}{\mathrm{N}}^{\mathrm{r}}\mathrm{and}{\mathrm{D}}^{\mathrm{r}} \\ \frac{1-{\displaystyle \frac{\mathrm{sin\theta }}{\mathrm{cos\theta }}}}{1+\frac{\mathrm{sin\theta }}{\mathrm{cos\theta }}}=\frac{1-\sqrt{3}}{1+\sqrt{3}} \\ \frac{1-\mathrm{tan\theta }}{1+\mathrm{tan\theta }}=\frac{1-\sqrt{3}}{1+\sqrt{3}} \\ \mathrm{comparing}\mathrm{we}\mathrm{get} \\ \mathrm{tan\theta }=\sqrt{3}=\tan 60 \\ \mathrm{so}\mathrm{\theta }=60\mathrm{degree} \end{gathered}$$