Question

if coso-sino=√2sino, hence prove that coso+sino=√2coso ?
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Answer 1

Solution :

In triangle ABC ,

Here I am using angle A .

cosA + sinA = √2 cosA

Do the square both sides ,

( cosA + sinA )² = ( √2 cosA )²

=> cos²A+sin²A + 2cosAsinA = 2cos²A

=> sin²A+2cosAsinA=2cos²A -cos²A

=> sin²A = cos²A - 2cosAsinA

=>sin²A+sin²A =cos²A+sin²A-2cosAsinA

=> 2sin²A = ( cosA - sinA )²

=> √(2sin²A ) = √(cosA-sinA)²

=> √2 sinA = cosA - sinA

Therefore ,

cosA - sinA = √2 sinA

hence proved mark me as brainliest