Simplify 1-1/(csc(x)^2)

Problem

1−1/csc2(x)

Solution

1. Identify the reciprocal identity for the cosecant function, which states that sin(x)=1/csc(x)

2. Substitute the identity into the expression by replacing 1/csc2(x) with sin2(x)

1−sin2(x)

3. Apply the Pythagorean identity sin2(x)+cos2(x)=1 which can be rearranged to show that 1−sin2(x)=cos2(x)

cos2(x)

Final Answer

1−1/csc2(x)=cos2(x)

Want more problems? Check here!