Step-by-step Solution

Prove the trigonometric identity $\frac{\cot\left(x\right)}{\csc\left(x\right)}=\cos\left(x\right)$

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Step-by-step explanation

Problem to solve:

$\cot\left(x\right)\div\csc\left(x\right)=\cos\left(x\right)$

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

$\frac{\frac{1}{\tan\left(x\right)}}{\csc\left(x\right)}=\cos\left(x\right)$

Unlock this full step-by-step solution!

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (cot(x)/(csc(x)=cos(x). Applying the trigonometric identity: \cot\left(\theta\right)=\frac{1}{\tan\left(\theta\right)}. Divide fractions \frac{\frac{1}{\tan\left(x\right)}}{\csc\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}. Applying the trigonometric identity: \tan\left(\theta\right)\cdot\csc\left(\theta\right)=\sec\left(\theta\right). Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}.

Final Answer

true
$\cot\left(x\right)\div\csc\left(x\right)=\cos\left(x\right)$

Related formulas:

2. See formulas

Steps:

6

Time to solve it:

~ 0.06 s (SnapXam)