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

Use Basic Trigonometric Identities To Simplify The Expression Tan X Cot X class=

Sagot :

-1

Explanation

let's remember the indentities

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

so

Step 1

let the expression

[tex]-tan(-x)cot(-x)=?[/tex]

rewrite the expression:

replace using the identity

[tex]\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}[/tex]

therefore, the answer is

-1

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