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If sin x + cos x =√2cos x then prove that cos x - sin x = √2 sin x
If sin x + cos x =√2cos x then prove that cos x - sin x = √2 sin x

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4 years ago

```							sinx+cosx=21/2cosx=> sinx=(21/2-1)cosx=> tanx=(21/2-1).For Other:-We’ve to prove cosx-sinx=21/2sinx.OR We can prove this:- cosx=(21/2+1)sinxOR We can prove this:- cotx=(21/2+1).ORIGINALLY we had proved:- tanx=(21/2-1)=> cotx=1/(21/2-1)On Rationalising we get:cotx=(21/2+1), which is the required proof.
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4 years ago
```							Cos x + sin x = √2 cos xSin x = (√2-1)cos xMultiplying both sides with (√2+1), we get(√2+1)sin x = (√2+1)(√2-1)cos x√2 sin x + sin x = cos xCos x - sin x = √2 sin x
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2 years ago 616 Points
```							Dear student,Please find the answer to your question. cos x + sin x = √2 cos xSin x = (√2-1)cos xMultiplying both sides with (√2+1),we get(√2+1)sin x = (√2+1)(√2-1)cos x√2 sin x + sin x = cos xcos x - sin x = √2 sin x Thanks and regards,Kushagra
```
5 months ago
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