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Grade: 12th pass
```
Show that 2 sin2β + 4 cos (α + β) sin α sin β + cos 2 (α + β) = cos 2α.
Show that 2 sin2β + 4 cos (α + β) sin α sin β + cos 2 (α + β) = cos 2α.

```
3 months ago

## Answers : (1)

Anand Kumar Pandey
askIITians Faculty
2937 Points
```							Welcome to AskIITiansassuming your question to be2 sin^2β + 4 cos (α + β) sin α sin β + cos 2 (α + β) = cos 2α.LHS = 2 sin^2β + 4 cos (α + β) sin α sin β + cos 2(α + β)= 2 sin^2β + 4 (cos α cos β – sin α sin β) sin α sin β + (cos 2α cos 2β – sin 2α sin 2β)= 2 sin^2β + 4 sin α cos α sin β cos β – 4 sin^2α sin^2β + cos 2α cos 2β – sin 2α sin 2β= 2 sin^2β + sin 2α sin 2β – 4 sin^2α sin^2β + cos 2α cos 2β – sin 2α sin 2β= (1 – cos 2β) – (2 sin^2α) (2 sin^2β) + cos 2α cos 2β= (1 – cos 2β) – (1 – cos 2α) (1 – cos 2β) + cos 2α cos 2β= cos 2α= RHSTherefore, 2 sin^2β + 4 cos (α + β) sin α sin β + cos 2 (α + β) = cos 2αThanks
```
3 months ago
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