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** Step-by-step Solution **

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

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

$\frac{\cos\left(x\right)}{1+\sin\left(x\right)}$

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (1-sin(x))/cos(x)=cos(x)/(1+sin(x)). Starting from the right-hand side (RHS) of the identity. Multiply and divide the fraction \frac{\cos\left(x\right)}{1+\sin\left(x\right)} by the conjugate of it's denominator 1+\sin\left(x\right). Multiplying fractions \frac{\cos\left(x\right)}{1+\sin\left(x\right)} \times \frac{1-\sin\left(x\right)}{1-\sin\left(x\right)}. The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: (a+b)(a-b)=a^2-b^2..

** Final Answer

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