Question

Determine whether the following equation is identity or not:

$\mathrm{cot\theta }+\mathrm{sec\theta }=\mathrm{cosec\theta sec\theta }$.

Answer 1

Verify L.H.S and R.H.S at any value of $\mathit{\theta }$

$\mathrm{cot\theta }+\mathrm{sec\theta }=\mathrm{cosec\theta sec\theta }$

Let, $\mathrm{L}.\mathrm{H}.\mathrm{S}.=\mathrm{cot\theta }+\mathrm{sec\theta }$

when $\mathrm{\theta }={30}^{\circ }$

$\mathrm{L}.\mathrm{H}.\mathrm{S}.=\cot {30}^{\circ }+\sec {30}^{\circ }$

$$\begin{gathered} =\sqrt{3}+\frac{2}{\sqrt{3}} \\ =\frac{3+2}{\sqrt{3}} \\ =\frac{5}{\sqrt{3}} \end{gathered}$$

$\mathrm{R}.\mathrm{H}.\mathrm{S}.=\mathrm{cosec}{30}^{\circ }\sec {30}^{\circ }$

$$\begin{gathered} =2\times \frac{2}{\sqrt{3}} \\ =\frac{4}{\sqrt{3}} \end{gathered}$$

$\mathrm{L}.\mathrm{H}.\mathrm{S}.\ne \mathrm{R}.\mathrm{H}.\mathrm{S}.$

Hence, the given equation is not an identity.