Final answer to the problem
Step-by-step Solution
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Starting from the left-hand side (LHS) of the identity
Applying the cosecant identity: $\displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}$
Learn how to solve trigonometric identities problems step by step online.
$\frac{\csc\left(x\right)}{\sin\left(x\right)}-1$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity csc(x)/sin(x)-1=cot(x)^2. Starting from the left-hand side (LHS) of the identity. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}. Divide fractions \frac{\frac{1}{\sin\left(x\right)}}{\sin\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}. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}.