Q100 / 180 · COMEDK 2016 · Mathematics

Which one of the following equations has no solution?

  • A
    $\sqrt{3} \sin \theta-\cos \theta=2$
  • B
    $\cos \theta+\sin \theta=\sqrt{2}$
  • Correct answer
    C
    $\operatorname{cosec} \theta \cdot \sec \theta=1$
  • D
    $\operatorname{cosec} \theta-\sec \theta=\operatorname{cosec} \theta \cdot \sec \theta$

Solution

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.

Hence, the correct answer is option: 'C'.

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