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COMEDK · Maths · 8. Trigonometric Ratios & Identities

Which one of the following equations has no solution?

  1. A \(\sqrt{3} \sin \theta-\cos \theta=2\)
  2. B \(\cos \theta+\sin \theta=\sqrt{2}\)
  3. C \(\operatorname{cosec} \theta \cdot \sec \theta=1\)
  4. D \(\operatorname{cosec} \theta-\sec \theta=\operatorname{cosec} \theta \cdot \sec \theta\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\operatorname{cosec} \theta \cdot \sec \theta=1\)

Step-by-step Solution

Detailed explanation

By option (c), \(\operatorname{cosec} \theta \cdot \sec \theta=1\) \(\sin \theta \cos \theta=1\) \(2 \sin \theta \cos \theta=2\) \(\sin 2 \theta=2\) As we know that range of \(\sin x\) is \([-1,1]\). Hence, this equation has no solution.