Question

Using Trigonometry identities prove
a) Root 1-sin² theeta / Root 1 - cos² theeta = cot theeta

Answer 1

$$\begin{gathered} \mathrm{LHS}=\frac{\sqrt{1-{\sin }^2\mathrm{\theta }}}{\sqrt{1-{\cos }^2\mathrm{\theta }}} \\ =\frac{\sqrt{{\cos }^2\mathrm{\theta }}}{\sqrt{{\sin }^2\mathrm{\theta }}} \\ =\frac{\cos \mathrm{\theta }}{\sin \mathrm{\theta }} \\ =\cot \mathrm{\theta } \\ =\mathrm{RHS} \end{gathered}$$