Question

How do you simplify $se{c}^{2}xco{t}^{2}x$ ?

Answer 1

Simplify the given expression ${\sec }^2{\mathrm{xcot}}^2\mathrm{x}$:

The given expression is ${\sec }^2{\mathrm{xcot}}^2\mathrm{x}$.

Simplify by converting to $\frac{\sin x}{\cos x}$:

$\begin{array}{rcl}{\sec }^2\left(\mathrm{x}\right)\times {\cot }^2\left(\mathrm{x}\right)& =& \frac{1}{{\cos }^2\left(\mathrm{x}\right)}\times \frac{{\cos }^2\left(\mathrm{x}\right)}{{\sin }^2\left(\mathrm{x}\right)}\\ & =& \frac{1}{{\sin }^2\left(\mathrm{x}\right)}\end{array}$

Remove the terms for ${\cos }^2\left(\mathrm{x}\right)$

$\text{And}\frac{1}{{\sin }^2\left(\mathrm{x}\right)}={\csc }^2\left(\mathrm{x}\right)$

Hence, the obtained result is ${\csc }^2\left(\mathrm{x}\right)$.