# Step-by-step Solution

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## Step-by-step Solution

Problem to solve:

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

Solving method

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. Combine fractions with different denominator using the formula: \displaystyle\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d + b\cdot c}{b\cdot d}. When multiplying two powers that have the same base (\cos\left(x\right)), you can add the exponents. Apply the trigonometric identity: 1-\cos\left(x\right)^2=\sin\left(x\right)^2.

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

~ 0.06 s