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If Cosec A+Cot A=4, find Sin A?

  • Best Answer
    cosecA−cotA = (cosec²A−cot²A) / (cosecA+cotA) = 1/4
    ∴ 2cosecA = 4+1/4 = 17/4 ⟹ sinA = 8/17
    Indica · 0 0
  • Other Answer
  • -
    1/sinA + cosA/sinA = 4
    1 + cos A = 4 sin A
    sin A = (1/4) (1 + cos A)
    Como · 1 0
  • 1/sin(A) + cos(A)/sin(A) = 4 =>
    1 + cos(A) = 4*sin(A) =>
    cos(A) = 4*sin(A) - 1 =>
    cos^2(A) = 16*sin^2(A) - 8*sin(A) + 1 =>
    1 - sin^2(A) = 16*sin^2(A) + 8*sin(A) + 1 =>
    0 = 17*sin^2(A) + 8*sin(A) =>
    0 = [sin(A)]*[17*sin(A) + 8].

    The original equation indicates that sin(A) cannot be 0, so we conclude that
    sin(A) = -8/17.
    az_lender · 0 2
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