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The range of y such that the evaluation in x,y+cosx=sinx has a real solution

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An Intiative by Sri Chaitanya

a

−2,2

b

−2,2

c

−1,1

d

−12,12

answer is B.

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Detailed Solution

y=sinx−cosx =2(sinxcosπ4−cosxsinπ4) =2sin(x−π4)Since −1≤sin(x−π4)≤1 ⇒−2≤2sin(x−π4)≤2⇒−2≤y≤2

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