Kirsten Bishop

2022-11-26

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

Aleah Rowe

Expert

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 $\mathrm{sin}$and $\mathrm{cos}.$
$⇒1+co{t}^{2}x=\frac{{\mathrm{sin}}^{2}x}{{\mathrm{sin}}^{2}x}+\frac{{\mathrm{cos}}^{2}x}{{\mathrm{sin}}^{2}x}⇒1+co{t}^{2}x=\frac{{\mathrm{cos}}^{2}x+{\mathrm{sin}}^{2}x}{{\mathrm{sin}}^{2}x}⇒1+co{t}^{2}x=\frac{1}{{\mathrm{sin}}^{2}x}...\left[si{n}^{2}x+co{s}^{2}x=1\right]⇒1+co{t}^{2}x=\mathrm{cos}e{c}^{2}x$
Hence, the required answer is $1+co{t}^{2}x=\mathrm{cos}e{c}^{2}x$.

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