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

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Step-by-step Solution

Problem to solve:

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

Specify the solving method

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

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

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

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

Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity cot(x)sec(x)=csc(x). Apply the trigonometric identity: \displaystyle\cot(x)=\frac{\cos(x)}{\sin(x)}. Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}. Multiplying fractions \frac{\cos\left(x\right)}{\sin\left(x\right)} \times \frac{1}{\cos\left(x\right)}. Simplify the fraction \frac{\cos\left(x\right)}{\sin\left(x\right)\cos\left(x\right)} by \cos\left(x\right).

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Explore different ways to solve this problem

Prove from RHS (right-hand side)Express everything into Sine and Cosine
$\cot\left(x\right)\cdot\sec\left(x\right)=\csc\left(x\right)$

Main topic:

Trigonometric Identities

~ 0.04 s