Learn how to solve problems step by step online. Prove the trigonometric identity (csc(infinity)-1)/(csc(infinity)+1)=(1-sin(infinity))/(1+sin(infinity)). 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)}. Combine all terms into a single fraction with \sin\left(\infty\right) as common denominator. Divide fractions \frac{\frac{1-\sin\left(\infty\right)}{\sin\left(\infty\right)}}{\csc\left(\infty\right)+1} 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}.

Prove the trigonometric identity (csc(infinity)-1)/(csc(infinity)+1)=(1-sin(infinity))/(1+sin(infinity))