Please help with trigonometry?

If (2 sin(α-3π)+cos⁡(α-π/2)) / (sin⁡(3π/2+α)) = 2 , what is tan α?

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  • Vaman
    Lv 7
    1 month ago

    If (2 sin(α-3π)+cos⁡(α-π/2)) / (sin⁡(3π/2+α)) = 2 , what is tan α?

    sin(a-3 pi)= sin (a+pi -2pi) =sin (a+pi)= -sin a

    cos (a-pi/2)=sina

    sin(3pi/2+a) =sin (pi+(pi/2 +a))= - sin (pi/2+a)=-cos a. Put the values

    (-2 sin a +sin a)/-cos a= tan a=2,

    tan a=2

  • ?
    Lv 7
    1 month ago

    Using the appropriate compound angle identities:

    sin(a-3π) = sin(a)cos(3π) - cos(a)sin(3π) = -sin(a)cos(a-π/2) = cos(a)cos(π/2) + sin(a)sin(π/2) = sin(a)sin(3π/2+a) = sin(3π/2)cos(a) + cos(3π/2)sin(a) = -cos(a)

    Substituting these results into the original expression:

    [-2sin(a)+sin(a)]/[-cos(a)] = 2

    [-sin(a)]/[-cos(a)] = 2

    tan(a) = 2

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