Le `alphaa n dbeta` be such that `pi

Consider two complex numbers alphaa n dbeta as alpha=[(a+b i)//(a-b i)]^2+[(a-b i)//(a+b i)]^2, where a ,b , in R and beta=(z-1)//(z+1), w here |z|=1, then find the correct statement: both alphaa n dbeta are purely real both alphaa n dbeta are purely imaginary alpha is purely real andbeta is purely imaginary beta is purely real and alpha is purely imaginary

If (log)_(10)(1025)/(1024)=alphaa n d(log)_(10)2=beta , then the value of (log)_(10)4100 in terms of alphaa n dbeta is equal to alpha+9beta (b) alpha+12beta 12alpha+beta (d) 9alpha+beta

The value of a and b such that the function f(x)={(-2sinx"," , -pi le x le -(pi)/(2)),(a sinx+b",", -(pi)/(2) lt x lt (pi)/(2)),(cosx",", (pi)/(2) le x le pi ):} is continuous in [-pi,pi] are

Find alpha and beta, so the function f (x) defined by f(x) =-2 sin x, "for" -pi le x le-pi/2 =alpha sinx+beta"for" -pi/2lt x lt pi/2 =cosx , "for" pi/2 le x le pi, is continuous on [-pi, pi].

The value of a and b such that the function f(x) {:{(-2 sin x", "-pile x le -pi/2 ),(a sin x+b " ," -pi/2 lt x lt pi/2 ),(cos x", " pi/2 le x le pi ):} is continuous in [ - pi , pi ] are

If alphaa n dbeta,alphaa n dgamma,alphaa n ddelta are the roots of the equations a x^2+2b x+c=0,2b x^2+c x+a=0a d nc x^2+a x+2b=0, respectively, where a, b, and c are positive real numbers, then alpha+alpha^2= a.a b c b. a+2b+c c. -1 d. 0

Find the values of a and b so that the function f(x)={{:(x+asqrt2 sin x", "0 le x le pi//4),(2x cot x + b", "pi//4 le x le pi//2),(a cot 2x - b sin x", "pi//2 lt x le pi):} is continuous for 0 le x le pi .

for theta in [ 0, pi ] , let f( theta) = sin ( cos theta) and g ( theta) = cos ( sin theta ) . Let a = underset( 0 le theta le pi ) (" max") f ( theta) , b= underset(0 le theta le pi )( min) f( theta), c = underset(0 le theta le pi ) ( " max") g( theta) and d= underset( 0 le theta le pi )( min g( theta) . the correct inequalities satisfied by a,b,c,d are

Let P (n) be the statement C_(r) le n! for 1 le r le n then P(n + 1) = ________