Prove the trigonometric identity $\sec\left(x\right)=\sin\left(x\right)\left(\tan\left(x\right)+\cot\left(x\right)\right)$

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$\sin\left(x\right)\left(\tan\left(x\right)+\cot\left(x\right)\right)$

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity sec(x)=sin(x)(tan(x)+cot(x)). Starting from the right-hand side (RHS) of the identity. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\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.