Final Answer
true
Step-by-step Solution
Problem to solve:
$\csc\left(x\right)\cdot\tan\left(x\right)=\sec\left(x\right)$
Specify the solving method
1
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)}. Apply the trigonometric identity: \displaystyle\cot(x)=\frac{\cos(x)}{\sin(x)}.
Final Answer
true