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if sinA+cosA=1/5, then a value of tanA/2 satisfies which of the equation?
a. 2x^2-x-1
d. 2x^3-7x^2+2x+3=0

  • maths -

    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 (x-3)(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 (x-3)

    ( I know I should have been able to get tan A/2 = 3 without relying on my calculator,

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