The solution set of the equation cos-1x -sin-1x =sin-1(1-x) is ;
The solution set of the equation cos-1x -sin-1x =sin-1(1-x) is ;
(a) [-1, 1]
(b) [0, 1/2]
(c) [-1, 0]
(d) none of these
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cos-1x -sin-1x =sin-1(1-x)
=>cos-1x -(π/2-cos-1x) =sin-1(1-x) ;
=>2cos-1x =π/2+sin-1(1-x) ;
=>cos(2cos-1x) =cos(π/2+sin-1(1-x) );
=>2[coscos-1x]2-1 =-sinsin-1(1-x)
=> 2x2-1=-1+x
=>2x2-x=0
=> x(2x-1)=0
So x=0 and x=1/2
Hence option (b) is correct
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