(tan - sin)^2 + (1 - cos)^2 = (1 - sec)^2
tanx^2 - 2tanxsinx + sin^2x + 1 - 2cosx + cos^2x = 1 - 2secx + sec^2x =
tan^2x - 2tanxsinx + 1 + sin^2x + cos^2x - 2cosx = 1 + sec^2x - 2secx
tan^2x - 2 tanxsinx - 2cosx + 1 + 1 = 1 + sec^2x - 2secx [subtract 1 from each side]
tan^2x + 1 - 2tanxsinx - 2cosx = sec^2x - 2secx [tan^2x + 1 = sec^2x]
sec^2x - 2tanxsinx - 2cosx = sec^2x - 2sec [ subtract sec^2x from both sides, add 2cosx to each side]
-2tanxsinx = 2cosx - 2secx [divide both sides by -2]
tanxsinx = secx - cosx
(sinx/cosx) * sinx = secx - cosx
(sin^2x)cosx = (1/cosx) - cosx [sin^2x = 1 - cos^2x ......get a common denominator on the right]
(1 -cos^2x)/cosx = (1 -cos^2x)/cosx
(tan - sin)^2 + (1 - cos)^2 = (1 - sec)^2
tanx^2 - 2tanxsinx + sin^2x + 1 - 2cosx + cos^2x = 1 - 2secx + sec^2x =
tan^2x - 2tanxsinx + 1 + sin^2x + cos^2x - 2cosx = 1 + sec^2x - 2secx
tan^2x - 2 tanxsinx - 2cosx + 1 + 1 = 1 + sec^2x - 2secx [subtract 1 from each side]
tan^2x + 1 - 2tanxsinx - 2cosx = sec^2x - 2secx [tan^2x + 1 = sec^2x]
sec^2x - 2tanxsinx - 2cosx = sec^2x - 2sec [ subtract sec^2x from both sides, add 2cosx to each side]
-2tanxsinx = 2cosx - 2secx [divide both sides by -2]
tanxsinx = secx - cosx
(sinx/cosx) * sinx = secx - cosx
(sin^2x)cosx = (1/cosx) - cosx [sin^2x = 1 - cos^2x ......get a common denominator on the right]
(1 -cos^2x)/cosx = (1 -cos^2x)/cosx