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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

Grade:11

3 Answers

Kshitij K
44 Points
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)sinx
OR 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.
 
Shruti Singh
13 Points
3 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
Kushagra Madhukar
askIITians Faculty 629 Points
11 months ago
Dear student,
Please find the answer to your question.
 
cos x + sin x = √2 cos x
Sin x = (√2-1)cos x
Multiplying both sides with (√2+1),we get
(√2+1)sin x = (√2+1)(√2-1)cos x
√2 sin x + sin x = cos x
cos x - sin x = √2 sin x
 
Thanks and regards,
Kushagra
 

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