Establish the identity csc theta 1csc theta 1 cot2 theta Mu

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

starting with left side

(csc theta - 1)( csc theta+1)

csc^2 theta + csc theta -csc theta -1

csc^2theta-1

cot^2 theta

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