Simplify the trigonometric expression sec(-x)tan(-x)cos(-x)

 Exercise

$sec\left(-x\right)tan\left(-x\right)cos\left(-x\right)$

 

Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$

$\frac{1}{\cos\left(-x\right)}\tan\left(-x\right)\cos\left(-x\right)$

 

Multiplying the fraction by $\tan\left(-x\right)\cos\left(-x\right)$

$\frac{\tan\left(-x\right)\cos\left(-x\right)}{\cos\left(-x\right)}$

 

Simplify the fraction $\frac{\tan\left(-x\right)\cos\left(-x\right)}{\cos\left(-x\right)}$ by $\cos\left(-x\right)$

$\tan\left(-x\right)$

 

Use the odd-even identity $\tan(-\theta)=-\tan(\theta)$

$-\tan\left(x\right)$

$-\tan\left(x\right)$

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