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Sin^-1(1-x)-2sin^-1(x)=(π÷2) then find the value of x

Sin^-1(1-x)-2sin^-1(x)=(π÷2) then find the value of x

Grade:12

1 Answers

Arun
25763 Points
3 years ago
Dear Vaibhav
 
Sin^-1(1-x) = (pi/2) + 2 sin^-1(x)
(1-x) = sin[pi/2 +(2sin^-1(x)]
1-x = cos (2 sin^-1(x))
On changing sin^-1 x to cos ^-1 x, and further solving
1-x = 1-2 x²
2 x² -x = 0
x = 0  and  x = ½
But for x = 1/2 , LHS is not equal to RHS.
Hence 
x = 0 is the solution.
 
Regards
Arun (askIITians forum expert)
 

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