# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

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

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

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

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

### Main topic:

Trigonometric Identities

9

### Time to solve it:

~ 0.05 s (SnapXam)