For `0sin(cosx)`

sin2x+cosx=0

lim_(xto0)(sin[cosx])/(1+[cosx]) , ([.] denotes the greatest integer function)

lim_(x rarr0)(sin x+cosx)^(1/(2x))

For 0ltxlt(pi)/(2) ,prove that x gt sin x and hence cos (sin x) gt sin (cosx)

Slove (2sinx-cosx)(1+cosx)=sin^2x

int sin x d(cosx)=

Let 0ltalpha,beta,gammalt(pi)/2 are the solutions of the equations cosx=x,cos(sinx)=x and sin(cosx)=x respectively, then show that gammaltalphaltbeta .

If 0ltxlt(pi)/(2) exp [(sin^(2)x+sin^(4)x+sin^(6)x+'.....+oo)log_(e)2] satisfies the quadratic equation x^(2)-9x+8=0 , find the value of (sinx-cosx)/(sinx+cosx) .

sin^(-1)(cosx)=