Answer:
Below.
Step-by-step explanation:
Convert to sines and cosines:
1 - [(sinxtanx/ (1+ secx)]
= 1 - [(sin^2x/ cos x) / ( 1 + 1/cosx)]
= 1 - [ (sin^2 x / cos x) / (cos x + 1 / cos x)]
= 1 - [(sin^2 x / cos x) * (cosx / (cosx + 1)]
= 1 - ( sin^2 x / (cos x + 1) Using sin^2x = 1 - cos^2 x:
= 1 - (1 - cos^2x) /( cos x + 1) Using difference of 2 squares:
= 1 - [(1 + cos x)(1 - cos x)] / (1 + cos x) The (1 + cos x) is common so:
= 1 - (1 - cos x)
= 1 - 1 + cos x
= cos x.
