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Question: Answered & Verified by Expert
Which one of the following equations has no solution?
MathematicsTrigonometric Ratios & IdentitiesCOMEDKCOMEDK 2016
Options:
  • A $\sqrt{3} \sin \theta-\cos \theta=2$
  • B $\cos \theta+\sin \theta=\sqrt{2}$
  • C $\operatorname{cosec} \theta \cdot \sec \theta=1$
  • D $\operatorname{cosec} \theta-\sec \theta=\operatorname{cosec} \theta \cdot \sec \theta$
Solution:
1478 Upvotes Verified Answer
The correct answer is: $\operatorname{cosec} \theta \cdot \sec \theta=1$
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.

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