((2))/((2)sin^(2)x^(2/3)+x^(1/3)-2=0)

2sin^(2)x+sqrt(3)cos x+1=0

lim_(x rarr0)(sin^(-1)x+3x)/(tan x+2sin((1)/(2)sin^(-1)x)[3-4sin^(2)((1)/(2)sin^(-1)x)])=

int(cos x)/([cos((x)/(2))+sin((x)/(2))]^(5))dx= 1) (2)/(3)[cosec((x)/(2))+sec((x)/(2))]^(3) 2) (2)/(3)[cos((x)/(2))+sin((x)/(2))]^(3)+C 3) (2)/(3)[sin((x)/(2))-cos((x)/(2))]^(3)+c 4) -(1)/(3)[sin((x)/(2))+cos((x)/(2))]^(-3)

Lt_(x to 0)(sin^(-1)x+3x)/(tanx+2sin((1)/(2)sin^(-1)x)[3-4"sin"^(2)((1)/(2)sin^(-1)x)])=

Solve sin^(2)x+(1)/(4)sin^(2)3x=sin x sin^(2)3x

sin^(3)x +sin^(3)(x-(2pi)/3) +sin^(3)(x+(2pi)/3)=0

If A(x_1,y_1),B(x_2,y_2) and C(x_3,y_3) are the vertices of traingle ABC and x_(1)^(2)+y_(1)^(2)=x_(2)^(2)+y_(2)^(2)=x_3^(2)+y_(3)^(2) , then show that x_1 sin2A+x_2sin2B+x_3sin2C=y_1sin2A+y_2sin2B+y_3sin 2C=0 .

If A(x_1,y_1),B(x_2,y_2) and C(x_3,y_3) are the vertices of traingle ABC and x_(1)^(2)+y_(1)^(2)=x_(2)^(2)+y_(2)^(2)=x_3^(2)+y_(3)^(2) , then show that x_1 sin2A+x_2sin2B+x_3sin2C=y_1sin2A+y_2sin2B+y_3sin 2C=0 .

If A(x_1,y_1),B(x_2,y_2) and C(x_3,y_3) are the vertices of traingle ABC and x_(1)^(2)+y_(1)^(2)=x_(2)^(2)+y_(2)^(2)=x_3^(2)+y_(3)^(2) , then show that x_1 sin2A+x_2sin2B+x_3sin2C=y_1sin2A+y_2sin2B+y_3sin 2C=0 .

Lt_(x to 0) (1-cos(2x^(3)))/(x^(2). tan^(2)3x.sin^(2)4x)=