Simplify the trigonometric expression tan(x)/(csc(x)sec(x))

 Exercise

$\frac{\tan\left(x\right)}{\csc\left(x\right)\cdot\sec\left(x\right)}$

 

Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$

$\frac{\frac{\sin\left(x\right)}{\cos\left(x\right)}}{\csc\left(x\right)\sec\left(x\right)}$

 Why is tan(x) = sin(x)/cos(x) ?

 

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

$\frac{\frac{\sin\left(x\right)}{\cos\left(x\right)}}{\csc\left(x\right)\frac{1}{\cos\left(x\right)}}$

 

Multiplying the fraction by $\csc\left(x\right)$

$\frac{\frac{\sin\left(x\right)}{\cos\left(x\right)}}{\frac{\csc\left(x\right)}{\cos\left(x\right)}}$

 

Simplify the fraction $\frac{\frac{\sin\left(x\right)}{\cos\left(x\right)}}{\frac{\csc\left(x\right)}{\cos\left(x\right)}}$

$\frac{\sin\left(x\right)}{\csc\left(x\right)}$

$\frac{\sin\left(x\right)}{\csc\left(x\right)}$

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