Question

The ${\theta }_1,{\theta }_2,{\theta }_3,{\theta }_4$ are the roots of the equation $\sin (\theta +\alpha )=k\sin 2\theta$, no two of which differ by multiple of $2\pi$, then ${\theta }_1+{\theta }_2+{\theta }_3+{\theta }_4$ is equal to

• A. $2n\pi ,nϵZ$
• B. $(2n+1)\pi ,nϵZ$
• C. $n\pi ,nϵZ$
• D. $Noneofthese$

Answer 1

Answer: (A)

$2n\pi ,nϵZ$

$\sin (\theta +\alpha )=k\sin 2\theta$

$\sin \theta \cos \alpha +\cos \theta \sin \alpha =2k\sin \theta \cos \theta$

$\sin \theta =0=$

$\theta =2n\pi$ for all values

$\cos \alpha +\sin \alpha =2k\cos \theta$