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CBSE Class 11-science Answered

cos cubed x sin to the power of 2 x end exponent=sum from x equals 0 to n ofa subscript rsin(rx), for all x element of R, the find n, a1 and a2  
Asked by aahnik.mohanty | 22 May, 2019, 10:15: PM
answered-by-expert Expert Answer
cos cubed x space sin 2 x space equals space stack sum space with r equals 0 below and n on top space a subscript r space sin left parenthesis r x right parenthesis N o w comma space stack sum space with r equals 0 below and n on top space a subscript r space sin left parenthesis r x right parenthesis equals a subscript 1 space sin x plus a subscript 2 space sin left parenthesis 2 x right parenthesis plus a subscript 3 space sin left parenthesis 3 x right parenthesis plus... plus a subscript n space sin left parenthesis n x right parenthesis space space a n d space sin left parenthesis 2 x right parenthesis equals 2 sin x cos x comma space w e space h a v e cos cubed x space sin 2 equals cos cubed x space open parentheses 2 sin x cos x close parentheses equals 2 space cos to the power of 4 x space sin x equals 2 space open parentheses cos squared x close parentheses squared space sin x equals 1 half space open parentheses 1 plus cos left parenthesis 2 x right parenthesis close parentheses squared space sin x equals 1 half space open parentheses 1 plus 2 cos left parenthesis 2 x right parenthesis plus cos squared left parenthesis 2 x right parenthesis close parentheses space sin x equals 1 half space open parentheses 1 plus 2 cos left parenthesis 2 x right parenthesis plus fraction numerator 1 plus cos 4 x over denominator 2 end fraction close parentheses space sin x equals 1 half space open parentheses 3 over 2 plus 2 cos left parenthesis 2 x right parenthesis plus fraction numerator cos 4 x over denominator 2 end fraction close parentheses space sin x equals 1 half space open parentheses 3 over 2 sin x plus 2 sin x space cos left parenthesis 2 x right parenthesis plus 1 half sin x space cos 4 x close parentheses equals 1 half space open parentheses 3 over 2 sin x plus left parenthesis sin left parenthesis x plus 2 x right parenthesis plus sin left parenthesis x minus 2 x right parenthesis right parenthesis plus 1 fourth left parenthesis sin left parenthesis x plus 4 x right parenthesis plus sin left parenthesis x minus 4 x right parenthesis right parenthesis close parentheses equals 1 half space open parentheses 3 over 2 sin x plus left parenthesis sin 3 x minus sin x right parenthesis plus 1 fourth left parenthesis sin left parenthesis 5 x right parenthesis minus sin left parenthesis 3 x right parenthesis right parenthesis close parentheses equals space 1 fourth sin x plus 3 over 8 sin 3 x plus 1 over 8 sin left parenthesis 5 x right parenthesis rightwards double arrow 1 fourth sin x plus 3 over 8 sin 3 x plus 1 over 8 sin left parenthesis 5 x right parenthesis equals a subscript 1 space sin x plus a subscript 2 space sin left parenthesis 2 x right parenthesis plus a subscript 3 space sin left parenthesis 3 x right parenthesis plus... plus a subscript n space sin left parenthesis n x right parenthesis E q u a t i n g space t h e space c o e f f i c i e n t s comma space w e space h a v e a subscript 1 equals 1 fourth comma space a subscript 2 equals 0 comma space a subscript 3 equals 3 over 8 comma space a subscript 4 equals 0 comma space a subscript 5 equals 1 over 8 comma space a subscript 6 equals a subscript 7 equals..... equals a subscript n equals 0
Answered by Renu Varma | 23 May, 2019, 11:11: AM

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