Prove the trigonometric identity sin(e)sec(e)=tan(e)

 Exercise

$\sin\left(e\right)\sec\left(e\right)=\tan\left(e\right)$

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Starting from the left-hand side (LHS) of the identity

$\sin\left(e\right)\sec\left(e\right)$

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

$\sin\left(e\right)\cdot \frac{1}{\cos\left(e\right)}$

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Multiplying the fraction by $\sin\left(e\right)$

$\frac{\sin\left(e\right)}{\cos\left(e\right)}$

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Apply the trigonometric identity: $\frac{\sin\left(\theta \right)}{\cos\left(\theta \right)}$$=\tan\left(\theta \right)$, where $x=e$

$\tan\left(e\right)$

 Why is sin(x)/cos(x) = tan(x) ?

 

Since we have reached the expression of our goal, we have proven the identity

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