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# Prove the trigonometric identity $\frac{\cos\left(x\right)}{1-\sin\left(x\right)}=\sec\left(x\right)+\tan\left(x\right)$

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true

##  Step-by-step Solution 

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

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

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

true

##  Explore different ways to solve this problem

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### Main Topic: Trigonometric Identities

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables where both sides of the equality are defined.