** Final Answer

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** Step-by-step Solution **

** Specify the solving method

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Starting from the right-hand side (RHS) of the identity

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Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$

**Why is tan(x) = sin(x)/cos(x) ?

Learn how to solve trigonometric identities problems step by step online.

$\sec\left(x\right)+\tan\left(x\right)$

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity cos(x)/(1-sin(x))=sec(x)+tan(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 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.

** Final Answer

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