If `Lt_(x->0)(1+asinx)^(cscx)=3`, then ` alpha` is

If 0 lt alpha lt (pi)/(3) , then prove that alpha (sec alpha) lt (2pi)/(3).

If 0 lt alpha lt (pi)/(3) , then prove that alpha (sec alpha) lt (2pi)/(3).

If 0 lt alpha lt (pi)/(3) , then prove that alpha (sec alpha) lt (2pi)/(3).

If 0 lt alpha lt (pi)/(3) , then prove that alpha (sec alpha) lt (2pi)/(3).

Let f(x)={{:(x^(alpha)sin\ (1/x)sinpix\ \ \ ;\ \ x\ !=0),( 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ ;\ \ \ x=0):} If Rolles theorem is applicable to f(x) on [0,1] then range of alpha is (a) -oo lt alpha lt -1 (b) alpha=1 (c) -1 lt alpha lt oo (d) alpha ge 0

lt_(x->0)(alpha e^(x)-beta)/(x)=201. then find the values of 'alpha' and ^(x)beta'

If 0 lt alpha lt (pi)/(2) and sin alpha + cos alpha = sqrt2, then the value of cos 3 alpha is-

The value of the integral int_(0)^(pi) (xdx)/(1+cos alpha sinx), 0 lt alpha lt pi , is