<prompt> Tuseme kwamba sec xtan xfrac227. Pata csc xcot x.  <response>: Tunaweza kuandika equation iliyotolewa kamafrac1cos x fracsin xcos x frac1 sin xcos x frac227, kwa hivyo cos x frac722 1 sin x. Inabadilisha kuwa cos2 x sin2 x 1, tunapatafrac49484 1 sin x2 sin2 x 1.Hii hurahisisha hadi 533 sin2 x 98 sin x - 435 0, mambo ambayo ni sin x 1533 sin x - 435 0, hivyo sin x -1 au sin x frac435533. Ikiwa sin x -1, kisha cos x 0, ambayo hufanya sec x tan x kutofafanuliwa. Kwa hivyo, sin x frac435533, na cos x frac722 1 sin x frac308533.Kishacsc x cot x frac1sin x fraccos xsin x frac1 cos xsin x frac1 frac308533frac435533 frac2915. 