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

Question

Kshitij K · Answer

sinx+cosx=2 1/2 cosx => sinx=(2 1/2- 1)cosx => tanx=(2 1/2 -1). For Other:- We’ve to prove cosx-sinx=2 1/2 sinx. OR We can prove this:- cosx=(2 1/2 +1)sinx OR We can prove this:- cotx=(2 1/2 +1). ORIGINALLY we had proved:- tanx=(2 1/2 -1) => cotx=1/(2 1/2 -1) On Rationalising we get: cotx=(2 1/2 +1), which is the required proof.

Shruti Singh · Answer

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 · Answer

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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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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