Lf sin3xsin 3x-m-0nCmcosmx- where C0- C1- C2-Cn are constants and Cn- 0- then n-

The correct option is C 6 sin ^ 3 x sin 3x =∑ _ m=0 ^ n C _ m cos ^ m x #160; sin ^ 3 x ( 3sin x 4sin ^ 3 x #160; ) =∑ _ m=0 ^ n ...

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Byju's Answer

Standard XII

Mathematics

Determinant

lf sin3xsin...

Question

lf ${sin}^{3} x sin 3 x = n \sum m = 0 C_{m} {cos}^{m} x$ ; where $C_{0}, C_{1}, C_{2} \dots \dots . . C_{n}$ are constants and $C_{n} \neq 0,$ then $n =$

0

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Solution

The correct option is C $6$
${sin}^{3} x sin 3 x = \sum_{m = 0}^{n} C_{m} {cos}^{m} x$
${sin}^{3} x (3 sin x - 4 {sin}^{3} x) = \sum_{m = 0}^{n} C_{m} {cos}^{m} x$
$3 {sin}^{4} x - 4 {sin}^{6} x = \sum_{m = 0}^{n} C_{m} {cos}^{m} x$
$∴ n = 6$

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Similar questions

Q. If

s i n^{3} x s i n 3 x = \sum_{m = 0}^{n} C_{m} c o s m x

where

c_{0}, c_{1}, c_{2}, . . . . . . . . . . . c_{n}

are constants and

C_{n} \neq 0

,then the value of n is

$I f s i n^{3} x s i n 3 x = \sum_{m = 0}^{n} c_{m} c o s m x w h e r e c_{0}, c_{1}, c_{2} . \dots \dots, c_{n} a r e c o n s t a n t s a n d c_{n} \neq 0, t h e n t h e v a l u e o f n i s$

Q. If

{sin}^{3} x sin 3 x = C_{0} + C_{1} cos 2 x + C_{2} cos 4 x + \dots + C_{n} cos 2 n x

, where

C_{0}, C_{1} . . . . . . C_{n}

are constants and

(C_{n} \neq 0)

, then which of the following is/are correct?

$I f s i n^{3} x s i n 3 x = \sum_{m = 0}^{n} c_{m} c o s m x w h e r e c_{0}, c_{1}, c_{2} . \dots \dots, c_{n} a r e c o n s t a n t s a n d c_{n} \neq 0, t h e n t h e v a l u e o f n i s$

Q. If

C_{0}, C_{1}, C_{2}, . . . . ., C_{n}

are Binomial coefficients then find the value of

C_{0} + 2. C_{1} + 3. C_{2} + . . . . . + (n + 1) . C_{n} .

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lf sin3xsin3x=n∑m=0Cmcosmx; where C0,C1,C2……..Cn are constants and Cn≠0, then n=

The correct option is C 6sin3xsin3x=∑nm=0Cmcosmxsin3x(3sinx−4sin3x)=∑nm=0Cmcosmx3sin4x−4sin6x=∑nm=0Cmcosmx∴n=6

lf ${sin}^{3} x sin 3 x = n \sum m = 0 C_{m} {cos}^{m} x$ ; where $C_{0}, C_{1}, C_{2} \dots \dots . . C_{n}$ are constants and $C_{n} \neq 0,$ then $n =$

The correct option is C $6$
${sin}^{3} x sin 3 x = \sum_{m = 0}^{n} C_{m} {cos}^{m} x$
${sin}^{3} x (3 sin x - 4 {sin}^{3} x) = \sum_{m = 0}^{n} C_{m} {cos}^{m} x$
$3 {sin}^{4} x - 4 {sin}^{6} x = \sum_{m = 0}^{n} C_{m} {cos}^{m} x$
$∴ n = 6$