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)`

(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)

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 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

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

Find the amplitude of sinalpha+i(1-cosalpha)

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

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

If F (alpha)= [{:(cosalpha,0, sinalpha),(0,1,0),(-sinalpha,0,cosalpha):}] Show that = F (alpha)^(-1)= F(-alpha)

Consider the matrix A_(alpha)=[(cosalpha,-sinalpha),(sinalpha,cosalpha)] Show that A_(alpha)A_(beta)=A_(alpha+beta)

If "cot"(alpha+beta)=0, then "sin"(alpha+2beta) can be (a) -sinalpha (b) sinbeta (c) cosalpha (d) cosbeta