maths
posted by shreya on .
if sinA+cosA=1/5, then a value of tanA/2 satisfies which of the equation?
a. 2x^2x1
b.x^22x3=0
c.2x^25x3=0
d. 2x^37x^2+2x+3=0

sinA+cosA=1/5
square both sides
sin^2A + 2sinAcosA + cos^2A = 1/25
2sinAcosA = 1/25  1 = 24/25
sin 2A = 24/25
setting my calculator to radians
2A = 4.4286 or 2A = 4.9962
A/2 = 1.10715 or A/2 = 1.249
so tan A/2 = 3.99999 or tan A/2 = 3
or tan A/2 = 0
clearly 0 does not work as a zero for any of the given equations, (they all have a constant)
tan A/2 = 3 does work in equation b)
which would factor to (x3)(x+1) = 0 to get a root of 3
3 is also a root of c) and d) since they both factor containing a factor of (x3)
( I know I should have been able to get tan A/2 = 3 without relying on my calculator,