Simplifying trig expressions by using trig definitions, reciprocal relationships, and trig Pythagorean’ identities

Question

Sin x Csc x - Sin² x =

cos x (1 + tan² x ) =

tan² o / csc o + 1 =

1/cot² x + 1 =

Answer 1

sin csc - sin^2 = 1 - sin^2 = cos^2

cos ( 1 + tan^2) = cos (sec^2) = cos/cos^2 = 1/cos = sec

sin^2/cos^2 * 1/ sin + 1 =

sin/cos^2 + 1 =

(sin + cos^2) / cos^2

1/cot^2 + 1 = tan^2 + 1 = sec^2