Let $n$ be an odd integer. If $\sin \,\,n{\rm{\theta }} = {\rm{\;}}\mathop \sum \limits_{r = 0}^n \,\,{b_r}\,\,{\sin ^r}\,\,{\rm{\theta \;}}$ for all real ${\rm{\theta }}$, then

${b_0} = 0,\,{b_1} = {n^2} - 3n - 3$

JEE MATHEMATICS MCQ: MULTIPLE AND SUBMULTIPLE ANGLES

1 Hard

1 of 1

Understanding +4 | -1

Let

n

be an odd integer. If

\sin \,\,n\mathrm{\theta } = \mathrm{\;}\sum \limits_{r = 0}^n \,\,{b_r}\,\,{\sin ^r}\,\,\mathrm{\theta \;}

for all real

\mathrm{\theta }

, then

View answer and explanation

Correct option: B

{b_{0 = }}0,\,\;{b_1} = n

Option B (

{b_{0 = }}0,\;{b_1} = n

) is correct because when

\mathrm{\theta } = 0

\sin n\mathrm{\theta } = 0

and the derivative at

\mathrm{\theta } = 0

gives

{b_1} = n