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

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true

##  Step-by-step Solution 

How should I solve this problem?

• Prove from RHS (right-hand side)
• Prove from LHS (left-hand side)
• Express everything into Sine and Cosine
• Exact Differential Equation
• Linear Differential Equation
• Separable Differential Equation
• Homogeneous Differential Equation
• Integrate by partial fractions
• Product of Binomials with Common Term
• FOIL Method
Can't find a method? Tell us so we can add it.
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Starting from the right-hand side (RHS) of the identity

$\frac{\cos\left(x\right)}{1+\sin\left(x\right)}$
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Multiply and divide the fraction $\frac{\cos\left(x\right)}{1+\sin\left(x\right)}$ by the conjugate of it's denominator $1+\sin\left(x\right)$

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

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..

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.

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