# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

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

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

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

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (sec(x)/(cot(x)+tan(x))=sin(x). Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}. Divide fractions \frac{\frac{1}{\cos\left(x\right)}}{\cot\left(x\right)+\tan\left(x\right)} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. Multiplying polynomials \cos\left(x\right) and \cot\left(x\right)+\tan\left(x\right). Applying the trigonometric identity: \tan\left(\theta\right)\cdot\cos\left(\theta\right)=\sin\left(\theta\right).

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

### Main topic:

Trigonometric Identities

12

### Time to solve it:

~ 0.05 s (SnapXam)