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

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$\frac{\sec\left(\infty\right)}{\tan\left(\infty\right)+\cot\left(\infty\right)}$

Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity sec(infinity)/(tan(infinity)+cot(infinity))=sin(infinity). Starting from the left-hand side (LHS) of the identity. Use the trigonometric identities: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)} and \displaystyle\cot\left(\theta\right)=\frac{\cos\left(\theta\right)}{\sin\left(\theta\right)}. Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}. The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors.