Establish the identity csc theta 1csc theta 1 cot2 theta

Establish the identity. (csc theta - 1)(csc theta + 1) = cot^2 theta Multiply and write the left side expression as the difference of two squares.

Solution

( csc(theta) +1)(csc(theta) -1) = cot^2(theta)

LHS :( csc(theta) +1)(csc(theta) -1)

= csc^2(theta) - 1

Use the identity : 1 + cot^2(x) = csc^2(x)

So, csc^2(theta) - 1 = cot^2(theta)

= RHS