Question

tan theta - cot theta = 2sin²theta-1/ sintheta x costheta

Answer 1

$$\begin{gathered} \mathrm{LHS}=\tan \mathrm{\theta }-\cot \mathrm{\theta } \\ =\frac{\sin \mathrm{\theta }}{\cos \mathrm{\theta }}-\frac{\cos \mathrm{\theta }}{\sin \mathrm{\theta }} \\ =\frac{{\sin }^2\mathrm{\theta }-{\cos }^2\mathrm{\theta }}{\sin \mathrm{\theta }.\cos \mathrm{\theta }} \\ =\frac{{\sin }^2\mathrm{\theta }-\left(1-{\sin }^2\mathrm{\theta }\right)}{\sin \mathrm{\theta }.\cos \mathrm{\theta }} \\ =\frac{2{\sin }^2\mathrm{\theta }-1}{\sin \mathrm{\theta }.\cos \mathrm{\theta }} \\ =\mathrm{RHS} \end{gathered}$$