Step-by-step Solution

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

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Final Answer

true

Step-by-step Solution

Problem to solve:

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

Choose the solving method

1

Applying the cosecant identity: $\displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}$

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

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

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

Unlock this full step-by-step solution!

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity csc(x)tan(x)=sec(x). Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}. Multiply the fraction and term. Simplify \frac{\tan\left(x\right)}{\sin\left(x\right)}. Since both sides of the equality are equal, we have proven the identity.

Final Answer

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

Related Formulas:

2. See formulas

Time to solve it:

~ 0.04 s