Step-by-step Solution

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

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

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)}. 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}. Simplify \sin\left(x\right)\cot\left(x\right) into \cos(x) applying trigonometric identities.