`("lim")_(nvecoo)"{"(n/(n+1))^(alpha)+sin(1/n)]^n`(when `alpha in Q`) is equal to (a) `e^(-alpha)` (b) `-alpha` (c) `e^(1-alpha)` (d) `e^(1+alpha)`

alpha beta x ^(alpha-1) e^(-beta x ^(alpha))

If cos^(-1)x-cos^(-1)y/2=alpha,t h e n4x^2-4x ycosalpha+y^2 is equal to (a)4 (b) 2sin^2alpha (c) -4sin^2alpha (d) 4sin^2alpha

The value of int_0^(pi/2) sin|2x-alpha|dx, where alpha in [0,pi], is (a) 1-cos alpha (b) 1+cos alpha (c) 1 (d) cos alpha

If alpha in (-(3pi)/2,-pi) , then the value of tan^(-1)(cotalpha)-cot^(-1)(tanalpha)+sin^(-1)(sinalpha)+cos^(-1)(cosalpha) is equal to (a) 2pi+alpha (b) pi+alpha (c) 0 (d) pi-alpha

If f(x)=x^(11)+x^9-x^7+x^3+1 and f(sin^(-1)(sin8)=alpha,alpha is constant, then f(tan^(-1)(t a n8) is equal to alpha (b) alpha-2 (c) alpha+2 (d) 2-alpha

lim_(alpha to 0) (sin (alpha^n))/((sin alpha)^(m))

Prove that sin4 alpha=4tan alpha (1- tan^(2)alpha)/((1+tan^2 alpha)^2

If sin alpha + cos alpha = b then sin 2 alpha is equal to . . . . .

lim_(alphato0)(sin(alpha^(n)))/((sinalpha)^(m))