Prove the following trigonometric identities

Question

(i)(1+cotx)^2 +(1-cotx)^2=2cosec^2x
(ii)cos(270degrees+theta)/cos(360degrees -theta)

Answer 1

(1+cotx)^2 = 1 + 2cotx + cot^2x
(1-cotx)^2 = 1 - 2cotx + cot^2x
add 'em up to get
2 + 2cot^2x
= 2(1+cot^2x)
= 2csc^2x