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

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$\frac{\cot\left(x\right)}{\sec\left(x\right)}+\sin\left(x\right)$

Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity cot(x)/sec(x)+sin(x)=csc(x). Starting from the left-hand side (LHS) of the identity. Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}. Divide fractions \frac{\cot\left(x\right)}{\frac{1}{\cos\left(x\right)}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}.