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KCET 2014 Math Solved Paper

Question : 35 of 60

Marks: +1, -0

If sin θ = sin α, then

$\frac{\theta+\alpha}{2}$ is any odd multiple of $\frac{\pi}{2}$ and $\frac{\theta-\alpha}{2}$ is any multiple of $\pi$
$\frac{\theta+\alpha}{2}$ is any even multiple of $\frac{\pi}{2}$ and $\frac{\theta-\alpha}{2}$ is any odd multiple of $\pi$
$\frac{\theta+\alpha}{2}$ is any multiple of $\frac{\pi}{2}$ and $\frac{\theta-\alpha}{2}$ is any odd multiple of $\pi$
$\frac{\theta+\alpha}{2}$ is any multiple of $\frac{\pi}{2}$ and $\frac{\theta-\alpha}{2}$ is any even multiple of $\pi$

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 π/2 and

\frac{\theta-\alpha}{2}

is any multiple of π 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 π/2

\frac{\theta-\alpha}{2}

is any multiple of π

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