Prove the trigonometric identity $\frac{\cos\left(\theta\right)\left(\tan\left(\theta\right)+\sin\left(\theta\right)\right)}{\sin\left(\theta\right)}=1+\cos\left(\theta\right)$

Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity (cos(t)(tan(t)+sin(t)))/sin(t)=1+cos(t). Starting from the left-hand side (LHS) of the identity. Apply the trigonometric identity: \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}=\cot\left(\theta \right), where x=\theta. Multiply the single term \cot\left(\theta\right) by each term of the polynomial \left(\tan\left(\theta\right)+\sin\left(\theta\right)\right). Applying the trigonometric identity: \tan\left(\theta \right)\cot\left(\theta \right) = 1.