Simplifique as expressões: (a) (1 + cosx)(1− cosx) (b) 1 + cotg2 x sec2 x (c) cosx− 1 secx− 1 (d) sen2 2x (1 + cos 2x)2 + 1 (e) cos2 2x− sen2 x (f...

(a) (1 + cosx)(1− cosx) = 1 - cos²x = sen²x (b) 1 + cotg²x/sec²x = (1 + cos²x/sen²x)/(1/cos²x) = cos²x + sen²x/cos²x = (1/cos²x) (c) cosx− 1/secx− 1 = (cosx-1)(1/cosx-1) = -sen²x/(cosx-1) (d) sen²2x/(1+cos²2x)² + 1 = sen²2x/(sen²2x)² + 1 = 1/(sen²2x) + 1 = (1+sen²2x)/(sen²2x) = (cos²2x+sen²2x)/(sen²2x) = cotg²2x + 1/sen²2x (e) cos²2x - sen²x = (cos²x - sen²x)² - 4sen⁴x = cos⁴x - 2cos²xsen²x + sen⁴x - 4sen⁴x = cos⁴x - 2cos²xsen²x - 3sen⁴x (f) tgx - cossecx(1-2cos²x)secx = tgx - cossecxsecx + 2cos³xsecx = tgx - 1/cosx + 2cos³x/cosx = tgx - secx + 2cos³x/cosx