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Grade: 11
        
How to apply telescopic series in series involving sine of angles
4 years ago

Answers : (3)

Akshay
185 Points
							
suppose your seies is : sin x + sin 2x + sin 3x..........sin nx,
multiply and divide by sin x/2,
use sin x * sin y = ½ * (cos(x-y) – cos(x+y) ),
sin x * sinx/2 = 0.5 * cos(x/2) – 0.5 * cos(1.5x),
sin 2x * sin x/2 = 0.5 * cos(1.5 x) – 0.5*cos(2.5 x),
sin 3x * sin x/2 = 0.5 * cos(2.5 x) – 0.5*cos(3.5 x),
and so on,      adding them all of the terms will get cancelled out.
4 years ago
Akshay
185 Points
							
or if you want to do it using exponentials,
write sin ax =1/2 * (eiax-e-iax),
u will get two geomtric series, one for +ve powers of exp, other for negative powers. apply sum of gm formula 
4 years ago
manu
36 Points
							
se sin x * sin y = ½ * (cos(x-y) – cos(x+y) ),
sin x * sinx/2 = 0.5 * cos(x/2) – 0.5 * cos(1.5x),
sin 2x * sin x/2 = 0.5 * cos(1.5 x) – 0.5*cos(2.5 x),
sin 3x * sin x/2 = 0.5 * cos(2.5 x) – 0.5*cos(3.5 x),
3 years ago
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