Prove the trigonometric identity $\frac{\tan\left(x\right)}{\sec\left(x\right)}=\sin\left(x\right)$

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

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity tan(x)/sec(x)=sin(x). Starting from the left-hand side (LHS) of the identity. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}. We can simplify the quotient of fractions \frac{\frac{\sin\left(x\right)}{\cos\left(x\right)}}{\frac{1}{\cos\left(x\right)}} by inverting the second fraction and multiply both fractions.