Final Answer
Step-by-step Solution
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Starting from the right-hand side (RHS) of the identity
Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$
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$\sec\left(x\right)-\tan\left(x\right)$
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.