Step-by-step Solution

Prove the trigonometric identity $\cot\left(x\right)\sec\left(x\right)=\csc\left(x\right)$

Go!
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Final Answer

true

Step-by-step Solution

Problem to solve:

$\cot\left(x\right)\cdot\sec\left(x\right)=\csc\left(x\right)$

Solving method

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Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$

$\frac{\cot\left(x\right)}{\cos\left(x\right)}=\csc\left(x\right)$
2

Apply the trigonometric identity: $\cot(x)=\frac{\cos(x)}{\sin(x)}$

$\frac{\frac{\cos\left(x\right)}{\sin\left(x\right)}}{\cos\left(x\right)}=\csc\left(x\right)$
3

Simplify the fraction $\frac{\frac{\cos\left(x\right)}{\sin\left(x\right)}}{\cos\left(x\right)}$ by $\cos\left(x\right)$

$\frac{1}{\sin\left(x\right)}=\csc\left(x\right)$
4

The reciprocal sine function is cosecant: $\frac{1}{\sin(x)}=\csc(x)$

$\csc\left(x\right)=\csc\left(x\right)$
5

Since both sides of the equality are equal, we have proven the identity

true

Final Answer

true
$\cot\left(x\right)\cdot\sec\left(x\right)=\csc\left(x\right)$

Related Formulas:

2. See formulas

Time to solve it:

~ 0.06 s