Question

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

Answer 1

Simplifying the expression $1-se{c}^{2}x$:

By the standard trigonometric identity, we know that:

$se{c}^{2}x-{\tan }^{2}x=1$, for any real number $x$.

Hence, we obtain :

$$\begin{gathered} 1-se{c}^{2}x=1-\left(1+{\tan }^{2}x\right)\left[\because se{c}^{2}x=1+{\tan }^{2}x\right] \\ =1-1-{\tan }^{2}x \\ =-{\tan }^{2}x \end{gathered}$$

Therefore, $1-se{c}^{2}x=-{\tan }^{2}x$.