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please trigonometry help

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 If sinx+cosx = 1/2, then tanx+cotx = ?

asked Jun 24, 2013 in TRIGONOMETRY by dkinz Apprentice

1 Answer

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The given trigonometric fuction value is sinx + cosx  = 1/2

tanx + cotx  = sinx / cosx + cosx /sinx

=( sin2x + cos2x )/ sinx cosx        [ sin2x + cos2x = 1]

= 1/ sinx cosx

sinx + cosx  = 1/2

Squareing on both side

(sinx + cosx)2  = (1/2)2

sin2x + cos2x +2 sinx cosx  = 1/4

1+ 2 sinx cosx = 1/4

2sinx cosx = - 3/4

sinx cosx  = - 3/8

tanx + cot x  = 1 / sinx cosx = 1/ ( -3/8) =  - 8/3.

answered Jun 24, 2013 by goushi Pupil

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