sin^(-1)(1-4)-2sin^(4)dx=(1)/(2)

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

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

2sin^(-1)(4/5)+sin^(-1)(24/25) = __.

int_(0)^( pi)sqrt(1+4sin^(2)((x)/(2))-2sin((x)/(2)))dx

If y=(1+sin x)(1+sin^(2)x)(1+sin^(4)x)(1+sin^(8)x)(1+sin^(16)x) ,then the value of (dy)/(dx) at x=0 is

int(sin4x)/(1+sin^(4)2x)dx=

int_(0)^( pi/2)(sin^(1/4)x)/(sin^(1/4)x+cos^(1/4)x)dx

y=sin^(-1)(3sin x-4sin^(3)x)" ,then "(dy)/(dx) at x= (sqrt(3))/(2) is

(d)/(dx)[sin^(-1)((2^(x+1))/(1+4^(x)))]