If the eqn sinx. (sinx + cosx) = k has real solution then , then find the range of k.

dear Sanchit

sinx. (sinx + cosx) = k

sin²x+sinx cosx=k

1/2- cos2x/2 +sin2x/2 =k

sin2x -cos2x=2k-1

 for real solution

-√2  ≤2k-1 ≤  √2   

(1-√2)/2  ≤k ≤ (1+ √2)/2

   
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