Q95 / 180 · KCET 2014 · Mathematics

If \( \sin \theta=\sin \alpha \), then

  • Correct answer
    A
    \( \frac{\theta+\alpha}{2} \) is any odd multiple of \( \frac{\Pi}{2} \) and \( \frac{\theta-\alpha}{2} \) is any multiple of
  • B
    \( \frac{\theta+\alpha}{2} \) is any even multiple of \( \frac{\Pi}{2} \) and \( \frac{\theta-\alpha}{2} \) is any odd multiple of \( I \)
  • C
    \( \frac{\theta+\alpha}{2} \) is any multiple of \( \frac{\Pi}{2} \) and \( \frac{\theta-\alpha}{2} \) is any odd multiple of
  • D
    \( \frac{\theta+\alpha}{2} \) is any multiple of \( \frac{\Pi}{2} \) and \( \frac{\theta-\alpha}{2} \) is any even multiple of

Solution

Given $\sin \theta=\sin \alpha$ $\sin \theta-\sin \alpha=0$ $2 \cos \left(\frac{\theta+\alpha}{2}\right) \sin \left(\frac{\theta-\alpha}{2}\right)=0$ It is not necessary that $\frac{\theta+\alpha}{2}$ is odd multiple of $\pi / 2$ and $\frac{\theta-\alpha}{2}$ is any multiple of $\pi$ should be simultaneous hold good for the above equation to be true Hence, the correct answer should be $\frac{\theta+\alpha}{2}$ is any odd multiple of $\pi / 2$ or $\frac{\theta-\alpha}{2}$ is any multiple of $\pi$

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

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