# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

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

$\frac{1-\sin\left(x\right)}{\cos\left(x\right)}=\frac{\cos\left(x\right)\left(1-\sin\left(x\right)\right)}{1-\sin\left(x\right)^2}$

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)). 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). Apply the trigonometric identity: 1-\sin\left(x\right)^2=\cos\left(x\right)^2. Simplify the fraction by \cos\left(x\right). Since both sides of the equality are equal, we have proven the identity.

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