Question

If cot theta =root 7 show that cosec ^2 theta -sec^2theta /cosec^2theta +sec^2theta =3/4

As given in the picture

Answer 1

.........make a triangle and apply formula

Answer 2

Answer:

Step-by-step explanation:

It is given that $cot{\theta}=\sqrt{7}$, therefore the values of $cosec{\theta}$ and $sec{\theta}$ are as follows:

$sec{\theta}=\frac{\sqrt{8}}{\sqrt{7}}$ and $cosec{\theta}=\sqrt{8}$.

Thus, the given equation becomes:

$\frac{cosec^{2}{\theta}-sec^{2}{\theta}}{cosec^{2}{\theta}+sec^{2}{\theta}}$

=$\frac{(\sqrt{8})^{2}-(\frac{\sqrt{8}}{\sqrt{7}})^2}{(\sqrt{8})^{2}+(\frac{\sqrt{8}}{\sqrt{7}})^2}$

=$\frac{8-\frac{8}{7}}{8+\frac{8}{7}}$

=$\frac{48}{64}=\frac{3}{4}$=RHS

Hence proved