A) \[-1\]
B) \[-2\]
C) 0
D) 1
E) 2
Correct Answer: B
Solution :
\[{{(cos\text{ }x+sin\text{ }x)}^{2}}+k\text{ }sin\text{ }x\text{ }cos\text{ }x-1=0\] \[\Rightarrow \] \[si{{n}^{2}}x+co{{s}^{2}}x+2\text{ }sin\text{ }x\text{ }cos\text{ }x+\] \[k\text{ }sin\text{ }x\text{ }cos\text{ }x-1=0\] \[\Rightarrow \]\[2\text{ }sin\text{ }x\text{ }cos\text{ }x=-k\text{ }sin\text{ }x\text{ }cos\text{ }x\] \[\Rightarrow \] \[k=-2\]
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