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

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Step-by-step Solution

Problem to solve:

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

Choose the solving method

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The tangent function is inverse to the cotangent: $\tan(x)=\frac{1}{\cot(x)}$

$\csc\left(x\right)\frac{1}{\cot\left(x\right)}=\sec\left(x\right)$

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

$\csc\left(x\right)\frac{1}{\cot\left(x\right)}=\sec\left(x\right)$

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity csc(x)tan(x)=sec(x). The tangent function is inverse to the cotangent: \tan(x)=\frac{1}{\cot(x)}. Multiply the fraction and term. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}. Divide fractions \frac{\frac{1}{\sin\left(x\right)}}{\cot\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}.

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

Main topic:

Trigonometric Identities

~ 0.04 s