Question

How do you simplify the expression $se{c}^{2}x-1$?

Answer 1

How to simplify the expression $se{c}^{2}x-1$:

The given expression is,

$se{c}^{2}x-1$

The cosine function is reciprocal of the secant function.

$\begin{array}{ccc}& & se{c}^{2}x-1=\frac{1}{{\cos }^{2}x}-1\\ & & =\frac{1-{\cos }^{2}x}{{\cos }^{2}x}\end{array}$

By using the identity, ${\sin }^{2}x+{\cos }^{2}x=1$.

$\begin{array}{ccc}& & se{c}^{2}x-1=\frac{{\sin }^{2}x}{{\cos }^{2}x}\\ & & ={\tan }^{2}x\end{array}$

Hence, the simplified form is $\mathit{t}\mathit{a}{\mathit{n}}^{\mathbf{2}}\mathit{x}$.