Question

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

Answer 1

-1

Step-by-step explanation

let's remember the indentities

`\begin{gathered} tan\theta=\frac{sen\text{ \lparen x\rparen}}{cos\text{ \lparen x\rparen}} \\ cot\theta=(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)=-(\sin(-x))/(cos(-x))*(cos(-x))/(\sin(-x)) \\ -tan(-x)cot(-x)=-(\sin(-x))/(sin(-x))(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