`(sqrt2-sinalpha-cosalpha)/(sinalpha-cosalpha)` is equal to (a)`sec(alpha/2-pi/8)` (b)`cos(pi/8-alpha/2)` (c)`tan(alpha/2-pi/8)` (d)`cot(alpha/2-pi/2)`

lim_(alphato pi/4)(sinalpha-cosalpha)/(alpha-pi/4) is

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)

(sinalpha+cosecalpha)^(2)+(cosalpha-secalpha)^(2)-tan^(2)alpha-cot^(2)alpha=?

The value of (sin(pi-alpha))/(sin alpha-cos alpha tan.(alpha)/(2))-cos alpha is

If cot^(-1)(sqrt(cosalpha))-tan^(-1)(sqrt(cosalpha))=x , then sinx is tan^2alpha/2 (b) cot^2alpha/2 (c) tan^2alpha (d) cotalpha/2

The value of the integral int_0^1(dx)/(x^2+2xcosalpha+1) is equal to (a) sinalpha (b) alphasinalpha (c) alpha/(2sinalpha) (d) alpha/2sinalpha

If cosbeta is the geometric mean between sinalphaa n dcosalpha, where 0ltalpha,betaltpi/ 2, then cos2beta is equal to(a) -2sin^2(pi/ 4-alpha) (b) -2cos^2(pi/ 4+alpha) (c) -2sin^2(pi/4+alpha) (d) 2cos^2(pi/ 4-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

the expression (1+sin2alpha)/(cos(2alpha-2pi)tan(alpha-(3pi)/4))-1/4sin2alpha(cot(alpha/2)+cot((3pi)/2+alpha/2)) simplifies and reduces to