please trigonometry help

Question

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

Answer 1

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.