Question

use basic trigonometric identities to simplify the expression: -tan (-x) cot (-x) = ?

Answer 1

-1

Explanation

let's remember the indentities

$\begin{gathered} tan\theta=\frac{sen\text{ \lparen x\rparen}}{cos\text{ \lparen x\rparen}} \\ cot\theta=\frac{cos(x)}{sin(x)} \end{gathered}$

so

Step 1

let the expression

$-tan(-x)cot(-x)=?$

rewrite the expression:

replace using the identity

$\begin{gathered} -tan(-x)cot(-x)=? \\ -tan(-x)cot(-x)=-\frac{\sin(-x)}{cos(-x)}*\frac{cos(-x)}{\sin(-x)} \\ -tan(-x)cot(-x)=-\frac{\sin(-x)}{sin(-x)}\frac{cos\left(-x\right)}{\sin(*x)} \\ -tan(-x)cot(-x)=-1*1 \\ -tan(-x)cot(-x)=-1 \end{gathered}$

therefore, the answer is

-1

I hope this helps you