2ln n'x=sin'(2x)/(1+x^(2))=cos(1-x^(3))/(1+x^(2))

IF 3 sin^(-1)((2x)/(1+x^(2)))-4cos^(-1)((1-x^(2))/(1+x^(2)))+ 2tan^(-1)((2x)/(1-x^(2)))=(pi)/3 then x=

3 sin ^(-1)((2 x)/(1+x^(2)))-4 cos ^(-1)((1-x^(2))/(1+x^(2))) +2 tan ^(-1)((2 x)/(1-x^(2)))=(pi)/(3) ( then ) x=

Range of the function f(x)=cos((ln(x^(2)+e))/(x^(2)+1))+sin(((ln(x^(2)+e))/(x^(2)+1))

Show that cos 2 x=cos ^(2) x-sin ^(2) x=2 cos ^(2) x-1=1-2 sin ^(2) x=(1-tan ^(2) x)/(1+tan ^(2) x)

cos x + cos2x + ... + cos nx = sin ((nx) / (2)) cos ec ((x) / (2)) cos (((n + 1) x) / (2))

int(sin2x)/(sin^(2)x+2cos^(2)x)dx(i)-log(1+sin^(2)x)+C(ii)log(1+cos^(2)x)+C( iii) -log(1+cos^(2)x)+C(iv)log(1+tan^(2)x)+C

int(sin2x)/(sin^(2)x+2cos^(2)x)dx(i)-log(1+sin^(2)x)+C(ii)log(1+cos^(2)x)+C( iii) -log(1+cos^(2)x)+C(iv)log(1+tan^(2)x)+C

lim_(n rarr0)(1-cos^(3)x+sin^(3)x+ln(1+x^(3))+ln(1+cos x))/(x^(2)-1+2cos^(2)x+tan^(4)x+sin^(3)x)

If y=x^(n){a cos(log x)+b sin(log x)}, prove that x^(2)(d^(2)y)/(dx^(2))+(1-2n)(dy)/(dx)+(1+n^(2))y=0