`lim_(x->2)((cosalpha)^x+(sinalpha)^x-1)/(x-2)`

Show that : lim_(xto4)((cosalpha)^(x)-(sinalpha)^(x)-cos2alpha)/(x-4)=cos^(4)alphalog_(e)(cosalpha)-sin^(4)alphalog_(e)(sinalpha)

The value of lim_(xto4)((cos alpha)^(x)-(sinalpha)^(x)-cos 2alpha)/(x-4), alpha epsilon(0,(pi)/2) is

The value of lim_(xto4)((cos alpha)^(x)-(sinalpha)^(x)-cos 2alpha)/(x-4), alpha epsilon(0,(pi)/2) is

The value of lim_(xto4)((cos alpha)^(x)-(sinalpha)^(x)-cos 2alpha)/(x-4), alpha epsilon(0,(pi)/2) is

The value of lim_(xto4)((cos alpha)^(x)-(sinalpha)^(x)-cos 2alpha)/(x-4), alpha epsilon(0,(pi)/2) is

If the lines represented by sin^(2)alpha(x^(2)+y^(2))=((cosalpha)x-(sinalpha)y)^(2) are perpendicular to each other, then alpha=

If π<α<3π2 then sqrt((1-cosalpha)/(1+cosalpha))+sqrt((1+cosalpha)/(1-cosalpha)) is equal to (a) 2/(sinalpha) (b) -2/(sinalpha) (c) 1/(sinalpha) (d) -1/(sinalpha)

If pi,t h e nsqrt((1-cosalpha)/(1+cosalpha))+sqrt((1+cosalpha)/(1-cosalpha)) is equal to 2/(sinalpha) (b) -2/(sinalpha) (c) 1/(sinalpha) (d) -1/(sinalpha)

prove that, |{:(0,cosalpha,-sinalpha),(sinalpha,0,cosalpha),(cosalpha,sinalpha,0):}|^2=|{:(" "1,x,-x),(" "x,1," "x),(-x,x," "1):}| where x= sinalpha cosalpha

A square of side ' a ' lies above the x-axis and has one vertex at the origin. The side passing through the origin makes an angle alpha (0ltalphaltpi/ 4) with the positive direction of x-axis. equation its diagonal not passing through origin is: a. y(cosalpha-sinalpha)-x(sinalpha-cosalpha)=a b. y(cosalpha+sinalpha)+x(sinalpha-cosalpha)=a c. y(cosalpha-sinalpha)+x(sinalpha+cosalpha)=a d. y(cosalpha+sinalpha)-x(cosalpha+sinalpha)=a