Let $n$ be an odd integer. If $\sin n\theta = \sum\limits_{r = 0}^n {{b_r}{{\sin }^r}\theta } $ for every value of $\theta $, then
Let $n$ be an odd integer. If $\sin n\theta = \sum\limits_{r = 0}^n {{b_r}{{\sin }^r}\theta } $ for every value of $\theta $, then
- A
${b_0} = 1,{b_1} = 3$
- B
${b_0} = 0,{b_1} = n$
- C
${b_0} = - 1,{b_1} = n$
- D
${b_0} = 0,{b_1} = {n^2} - 3n + 3$
Similar Questions
If $(1 + x) (1 + x + x^2) (1 + x + x^2 + x^3) ...... (1 + x + x^2 + x^3 + ...... + x^n)$
$\equiv a_0 + a_1x + a_2x^2 + a_3x^3 + ...... + a_mx^m$ then $\sum\limits_{r\, = \,0}^m {\,\,{a_r}}$ has the value equal to
If $(1 + x) (1 + x + x^2) (1 + x + x^2 + x^3) ...... (1 + x + x^2 + x^3 + ...... + x^n)$
$\equiv a_0 + a_1x + a_2x^2 + a_3x^3 + ...... + a_mx^m$ then $\sum\limits_{r\, = \,0}^m {\,\,{a_r}}$ has the value equal to
The number of terms in the expansion of $(1 +x)^{101} (1 +x^2 - x)^{100}$ in powers of $x$ is
The number of terms in the expansion of $(1 +x)^{101} (1 +x^2 - x)^{100}$ in powers of $x$ is
- [JEE MAIN 2014]
If $a$ and $d$ are two complex numbers, then the sum to $(n + 1)$ terms of the following series $a{C_0} - (a + d){C_1} + (a + 2d){C_2} - ........$ is
If $a$ and $d$ are two complex numbers, then the sum to $(n + 1)$ terms of the following series $a{C_0} - (a + d){C_1} + (a + 2d){C_2} - ........$ is
$\frac{{{C_0}}}{1} + \frac{{{C_1}}}{2} + \frac{{{C_2}}}{3} + .... + \frac{{{C_n}}}{{n + 1}} = $
$\frac{{{C_0}}}{1} + \frac{{{C_1}}}{2} + \frac{{{C_2}}}{3} + .... + \frac{{{C_n}}}{{n + 1}} = $
If $\sum\limits_{K = 1}^{12} {12K{.^{12}}{C_K}{.^{11}}{C_{K - 1}}} $ is equal to $\frac{{12 \times 21 \times 19 \times 17 \times ........ \times 3}}{{11!}} \times {2^{12}} \times p$ then $p$ is
If $\sum\limits_{K = 1}^{12} {12K{.^{12}}{C_K}{.^{11}}{C_{K - 1}}} $ is equal to $\frac{{12 \times 21 \times 19 \times 17 \times ........ \times 3}}{{11!}} \times {2^{12}} \times p$ then $p$ is