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Grade: 12th pass
```
What is the value of Cos0 x cos1 x cos2 x...........x cos89 = ?

```
2 years ago

## Answers : (2)

Arun
25185 Points
```							Dear student In between there will be a cos 90 degree too hence cos 90 = 0 now if 0 is multiplied in any number answer will be 0 Hence value of your question will be 0.  RegardsArun (askIITians forum expert)
```
2 years ago
Arun
25185 Points
```							Dear student Sorry I got your question in wrong way. Actual solution is as follows – Let Us Divide The Question Into Two PartsFirst Let Us Solve For Cosine Seriescos1. cos2. cos3 ..... cos89Let Us Club The First And Last Terms,then second and second last and so on(cos1. cos89) (cos2. cos88) (cos3 .cos87) .... (cos44. cos46) cos45cos45 will remain as no pairing will occurNowcos(90-x) = sinxApplying The Above formula In the series(cos1. sin1) (cos2. sin2) .... (cos44.sin44). cos45Similarly Doing For Sine Series(sin1. sin89) (sin2. sin88) (sin3. sin87) .... (sin44. sin46). sin45Applying sin(90-x) = cosx(sin1. cos1) (sin2. cos2) (sin3. cos3) .... (sin44. cos44). sin45Now We Know That Sin45 = Cos45So The Final Sine Series Becomes(cos1.sin1) (cos2.sin2) (cos3.sin3) .... (cos44. sin44). cos45  Which is exactly the same as cosine seriesThey are exactly same seriesso if we subtraction themAnswer= Zero
```
2 years ago
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