if `cos^(-1)((2)/(3x))+cos^(-1)((3)/(4x))=(pi)/2, x>3/4` then `x=` (a) `(sqrt(145))/(11)` (b) `(sqrt(145))/(12)` (c) `(sqrt(146))/(10)` (d) `(sqrt(146))/(11)`

cos^(-1)x sqrt(3)+cos^(-1)x=(pi)/(2)

If tan^(-1)x+2cot^(-1)x=(2 pi)/(3), then x, is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3)(d)sqrt(2)

If cos^-1( (x^2-1)/(x^2+1))+ tan^-1( (2x)/(x^2-1)) = (2pi)/3 , then x equal to (A) sqrt(3) (B) 2+sqrt(3) (C) 2-sqrt(3) (D) -sqrt(3)

If quad 3sin^(-1)((2x)/(1+x^(2)))-4cos^(-1)((1-x^(2))/(1+x^(2)))+2tan^(-2)((2x)/(1-x^(2)))=(pi)/(3),where|x|<1 then x is equal to (1)/(sqrt(3))(b)-(1)/(sqrt(3))(c)sqrt(3)(d)-(sqrt(3))/(4)

If 0

cos((3pi)/(4)+x)-cos((3pi)/(4)-x) = -sqrt(2)sinx

If |cos^(-1)((1-x^(2))/(1+x^(2)))|<(pi)/(3), then x in[-(1)/(3),(1)/(sqrt(3))] (b) x in[-(1)/(sqrt(3)),(1)/(sqrt(3))]x in[0,(1)/(sqrt(3))](d) none of these

f (x) = cos ((pi) / (sqrt (3)) sin x + sqrt ((2) / (3)) pi cos x)

sqrt(x-4)+3=sqrt(x+11)

If f(x)=sqrt(1+cos^(2)(x^(2))), then f'((sqrt(pi))/(2)) is (sqrt(pi))/(6)(b)-sqrt(pi/6)1/sqrt(6)(d)pi/sqrt(6)