Grade 12Algebra
how do the summation of sinx+sin3x+sin5x+.......+sin29x? could u please give a detailed explanation?
how do the summation of sinx+sin3x+sin5x+.......+sin29x? could u please give a detailed explanation?
1 Answer
nitish
there’s a direct formula for these type of questions ,it is:
S=sina+sin(a+b)+sin(a+2b)......+sin(a+(n-1)*b)= {sin(nb/2)*sin(a+ b*(n-1)/2) }/sin(b/2)
hence in your question, a=1x
b=2x and n=15
therefore the answer is: (substitue a,b,n in the formula)
{sin(15*2x/2)*(sin(x+7*2x))} / sinx
on solving you get the answer as:
{sin^2(15x)} / sinx
i hope you understand.
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