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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 $\displaystyle\cot\left(\theta\right)=\frac{\cos\left(\theta\right)}{\sin\left(\theta\right)}$
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$\frac{\sec\left(x\right)}{\cot\left(x\right)+\tan\left(x\right)}$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity sec(x)/(cot(x)+tan(x))=sin(x). 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.