Question

How do you simplify the expression $co{t}^{2}x+1$?

Answer 1

Simplify the given expression using the trigonometric identities.

We have to simplify the expression $co{t}^{2}x+1$.

Expressing the given expression in terms of $\sin$and $\cos .$

$$\begin{gathered} \Rightarrow 1+co{t}^{2}x=\frac{{\sin }^{2}x}{{\sin }^{2}x}+\frac{{\cos }^{2}x}{{\sin }^{2}x} \\ \Rightarrow 1+co{t}^{2}x=\frac{{\cos }^{2}x+{\sin }^{2}x}{{\sin }^{2}x} \\ \Rightarrow 1+co{t}^{2}x=\frac{1}{{\sin }^{2}x}\mathbf{}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{[}\mathbf{}\mathit{s}\mathit{i}{\mathit{n}}^{\mathbf{2}}\mathit{x}\mathbf{+}\mathit{c}\mathit{o}{\mathit{s}}^{\mathbf{2}}\mathit{x}\mathbf{=}\mathbf{1}\mathbf{]} \\ \Rightarrow 1+co{t}^{2}x=\cos e{c}^{2}x \end{gathered}$$

Hence, the required answer is $1+co{t}^{2}x=\cos e{c}^{2}x$.