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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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Answer» 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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