Question

Sin^6x-tan^6x=3tan^2sec^2x+1

Answer 1

Answer:

Step-by-step explanation:

sec6x - tan6x = (sec2x)3 - (tan2x)3

                  = (sec2x - tan2x)(sec4x + sec2xtan2x + tan4x)

                  = (1+tan2x-tan2x))[sec4x+sec2xtan2x+(sec2x-1)tan2x]

                  = sec4x - tan2x + 2sec2xtan2x

                  = sec2x(1+tan2x) - tan2x + 2sec2xtan2x

                  = sec2x - tan2x + sec2xtan2x + 2sec2xtan2x

                  = 1 + 3sec2xtan2x