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If \(\sin \theta+\cos \theta=\frac{\sqrt{7}}{2}\), then \((\sin \theta-\cos \theta)\) is equal to :

Question and options

If sin⁡θ+cos⁡θ=72\sin \theta+\cos \theta=\frac{\sqrt{7}}{2}, then (sin⁡θ−cos⁡θ)(\sin \theta-\cos \theta) is equal to :
  1. 0
  2. 12\frac{1}{2}
  3. 1
  4. 2\sqrt{2}

Answer and explanation

Correct answer: B - \(\frac{1}{2}\)
(sin+cos)^2 = 7/4 gives 2 sin cos = 3/4. (sin-cos)^2 = 1 - 3/4 = 1/4, so sin - cos = 1/2 (taking the positive root; 1/2 is the only matching option).

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