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Q.

Let 'a'denote the roots of equation coscos-1x+sin-1sin1+x22=2sec-1(secx) then possible values of [|10a|] where [.] denotes the  greatest integer function will be

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a

1

b

5

c

10

d

Both (1)  and ( 3)

answer is D.

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Detailed Solution

We have, x∈[-1,0]⇒x+1+x22=-2x⇒x2+6x+1=0⇒a=x=22-3⇒|10a|=|202-30|=30-202Also, x∈[0,1]⇒x+1+x22=2x⇒1+x2=2x⇒a=x=1⇒|10a|=10∴|10a|=10, 30-202⇒[|10a|]=1,10
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