# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

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

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

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

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

### Main topic:

Trigonometric Identities

18

### Time to solve it:

~ 0.16 s (SnapXam)