Step-by-step Solution

Prove the trigonometric identity $\tan\left(x\right)\cos\left(x\right)\csc\left(x\right)=1$

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Final Answer

true

Step-by-step Solution

Problem to solve:

$\tan\left(x\right)\cdot \cos\left(x\right)\cdot \csc\left(x\right)=1$

Choose the solving method

1

Apply the formula: $\cos\left(x\right)\csc\left(x\right)$$=\cot\left(x\right)$

$\cot\left(x\right)\tan\left(x\right)=1$

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

$\cot\left(x\right)\tan\left(x\right)=1$

Unlock this full step-by-step solution!

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

Final Answer

true
$\tan\left(x\right)\cdot \cos\left(x\right)\cdot \csc\left(x\right)=1$

Related Formulas:

2. See formulas

Time to solve it:

~ 0.06 s