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1978

JEE Main 1978 Mathematics question on Trigonometry

If tan⁡θ=−43\tan\theta = -\dfrac{4}{3}, then sin⁡θ\sin\theta is
  1. A.
    −45-\dfrac{4}{5} but not 45\dfrac{4}{5}
  2. B.
    −45-\dfrac{4}{5} or 45\dfrac{4}{5}
  3. C.
    45\dfrac{4}{5} but not −45-\dfrac{4}{5}
  4. D.
    None of the above
Show answer and solution

Correct option: B

Solution

Since tan θ = -4/3, θ lies in either the second quadrant (sin > 0, cos < 0) or the fourth quadrant (sin < 0, cos > 0). Using the identity sin²θ + cos²θ = 1 with tan θ = -4/3, we get sin θ = ±4/5. In Q2, sin θ = +4/5, and in Q4, sin θ = -4/5. Both values are valid since no additional restriction is placed on the quadrant, so sin θ can be either -4/5 or 4/5.

[1978]

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