a-maths!!!!!

a)sinA+cosA = 4/3
(sinA)(cosA) = k/3
(sinA+cosA)2 = 1+2sinAcosA
(4/3)2 = 1+2k/3
16/9 = 1+2k/3
7/9 = 2k/3
k = 7/6



(b)(sinA/1﹣cotA)+(cosA/ 1﹣tanA)
= (tanAsinA/tanA﹣1)+( cosA/ 1﹣tanA)
= -tanAsinA+cosA/( 1﹣tanA)
= (-sin2A+cos2A)/(cosA﹣sinA)
= cosA+sinA
= 4/3

sum of root=sinθ+cosθ=4/3
product of root=sinθ(cosθ)= -k/4
sinθ+cosθ=4/3
(sinθ+cosθ)^2=(4/3)^2
sinθ^2+cosθ^2+2sinθ(cosθ)=16/9
1+2(-k/4)=16/9
k= -14/9
b)sinθ+cosθ=4/3-----------(1)
sinθ(cosθ)= -k/4--------(2)
sinθ(cosθ)=7/18
from(1),sinθ=4/3-cosθ----------(3)
put(3)into (2), cosθ(4/3-cosθ)=7/18
4cosθ/3-cosθ^2-7/18=0
cosθ=0.431 or cosθ=0.902
when cosθ=0.431
sinθ+0.431=4/3
sinθ=0.902
when cosθ=0.902
sinθ=0.431
sinθ/(1-cotθ) + cosθ/(1-tanθ)
=sinθ/(sinθ-cosθ/sinθ)+cosθ/(cosθ-sinθ/cosθ)
=sinθ^2/(sinθ-cosθ)+cosθ^2/(cosθ-sinθ)
=(sinθ^2+cosθ^2)/(cosθ-sinθ)
=1/(cosθ-sinθ)
=2.12 or = -2.12