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Karthik Eyan Grade: 11
```        If tan (a+b-c) / tan (a-b+c) = tan c / tan b

What is the value of sin 2a + sin 2b + sin 2c.
```
7 years ago

## Answers : (1)

SAGAR SINGH - IIT DELHI
879 Points
```										Dear karthik,
Multiply through by cos(a-b+c).cos(b).cos(a-b+c).cos(c) …  sin(a+b-c)cos(a-b+c).sin(b).cos(c) − sin(a-b+c).cos(a+b-c).sin(c).cos(b) = 0  ½.sin(b).cos(c){ sin(2a) + sin(2b-2c) } − ½.sin(c).cos(b){ sin(2a) − sin(2b-2c) } = 0  ½.sin(2a).sin(b-c) + ½.sin(2b-2c){ sin(b).cos(c) + sin(c).cos(b) } = 0  ½.sin(2a).sin(b-c) + sin(b-c).cos(b-c).sin(b+c) = 0  ½.sin(2a).sin(b-c) + ½.sin(b-c){ sin(2b) + sin(2c) } = 0  ½.sin(b-c){ sin(2a) + sin(2b) + sin(2c) } = 0  ∴ sin(2a) + sin(2b) + sin(2c) = 0

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```
7 years ago
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