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`        How to apply telescopic series in series involving sine of angles`
4 years ago

```							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
```							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
```							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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