If `alpha+beta=90^@` and `alpha:beta=2:1` then `sinalpha:sinbeta=`

If cos alpha+cos beta=0=sin alpha+sinbeta, then cos2alpha+cos 2beta=

In alpha ge 0 ,betage0 and alpha+betalepi , then i) cos(alpha+beta) = cos alpha cosbeta-sinalpha sinbeta

In alpha ge 0 ,betage0 and alpha+betalepi , then ii) cos(alpha-beta) = cos alpha cosbeta+sinalpha sinbeta

If alpha,beta in (-pi/2,0) such that (sin alpha+sinbeta)+(sinalpha)/(sinbeta)=0 and (sinalpha+sinbeta) (sinalpha)/(sinbeta)=-1 and lambda=lim_(n->oo) (1+(2sinalpha)^(2n))/((2sinbeta)^(2n)) then :

If cosalpha+cosbeta=0=sinalpha+sinbeta, then cos2alpha+cos2beta is equal to (a) -2"sin"(alpha+beta) (b) -2cos(alpha+beta) (c) 2"sin"(alpha+beta) (d) 2"cos"(alpha+beta)

If cosalpha+cosbeta=0=sinalpha+sinbeta, then cos2alpha+cos2beta is equal to (a) -2"sin"(alpha+beta) (b) -2cos(alpha+beta) (c) 2"sin"(alpha+beta) (d) 2"cos"(alpha+beta)

Prove that |[cos alpha cos beta, cos alpha sin beta , sin alpha],[-sinbeta,cosbeta,0],[sinalpha cosbeta, sinalpha sinbeta, cos alpha]|=cos2alpha

If sinalpha-sinbeta=a and cosalpha+cosbeta=b then write the value of "cos"(alpha+beta) .

If cosalpha+cosbeta=1/3 and sinalpha+sinbeta=1/4 prove that cos(alpha-beta)/2=+-5/24

If sinalpha+sinbeta=1//2 and cosalpha+cosbeta=sqrt(3)//2 then 3beta+alpha =