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Question

If sin1(xx22+x34...)+cos1(x2x42+x64...)=π2 for 0<|x|<2,then x equal

A
12
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B
1
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C
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D
1
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Solution

The correct option is A 1
As we know that
Sum of an infinite GP is a1r for |r|<1

So xx22+x34=x1+x2

And also x2x22+x64=x21+x22

So sin1(xx22+x34)+cos1(x2x44+x64)=π2

sin1(x1+x2)=π2cos1(x21+x22)

sin1(2xx+2)=sin1(2x2x2+2)

1x+2=xx2+2

x2+2x=x2+2

2x=2

x=1

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