# 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.

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

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (sin(x)/(cos(x)+(cos(x)/(1+sin(x))=sec(x). Apply the identity: \frac{\sin\left(x\right)}{\cos\left(x\right)}=\tan\left(x\right). Combine \tan\left(x\right)+\frac{\cos\left(x\right)}{1+\sin\left(x\right)} in a single fraction. Multiplying polynomials \tan\left(x\right) and 1+\sin\left(x\right). Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}.

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

### Main topic:

Trigonometric Identities

15

### Time to solve it:

~ 0.08 s (SnapXam)