Let `cos^(-1)(x)+cos^(-1)(2x)+cos^(-1)(3x)b epidot`If `x`satisfies the equation `a x^3+b x^2+c x-c_1=0,`then the value of `(b-a-c)`is_________

Let `cos^(-1)(x)+cos^(-1)(2x)+cos^(-1)(3x)b epidot`If `x`satisfies the

1.	Let `cos^(-1)(x)+cos^(-1)(2x)+cos^(-1)(3x)b epidot`If `x`satisfies the equation `a x^3+b x^2+c x-c_1=0,`then the value of `(b-a-c)`is_________
Answer» Correct Answer - 3 `cos^(-1) (x) + cos^(-1) (2x) + cos^(-1) cos^(-1) (3x) = pi` or `cos^(-1) (2x) + cos^(-1) (3x)= pi - cos^(-1) (x) = cos^(-1) (-x)` or `cos^(-1) [(2x) (3x) - sqrt(1 -4x^(2)) sqrt(1 -9x^(2))] = cos^(-1) (-x)` or `6x^(2) - sqrt(1-4x^(2)) sqrt(1 -9x^(2)) = -x` or `(6x^(2) + x)^(2) = (1-4x^(2)) (1-9x^(2))` or `x^(2) + 12x^(3) = 1 - 13x^(2)` or `12x^(3) + 14x^(2) -1 = 0` `rArr a = 12, b = 14, c =0` `rArr a + b + c = 12 + 14 -1 = 25`

`tan^(-1)[(cosx)/(1+sinx)]`is equal to`pi/4-x/2,forx in (-pi/2,(3pi)/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-(3pi)/2,pi/2)`
The value of `sin^(-1)(sin12)+sin^(-1)(cos12)=`
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