# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

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

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (sin(x)/(cos(x)+(cos(x)/(1+sin(x))=sec(x). section:I. Choose what side of the identity to work on. To prove an identity, we usually begin to work on the side of the equality that seems to be more complicated, or the side that is not expressed in terms of sine and cosine. In this particular case, we will choose to work on the left side \frac{\sin\left(x\right)}{\cos\left(x\right)}+\frac{\cos\left(x\right)}{1+\sin\left(x\right)} to reach the right side \sec\left(x\right). section:II. Express in terms of sine and cosine. Express both sides of the identity in terms of sine (\sin(x)) and cosine (\cos(x)).

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### Problem Analysis

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

### Main topic:

Trigonometric Identities

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