If `0ltalphaltbetaltpi/2,` show that `(sinalpha)/alphagt(sinbeta)/beta`

Suppose alpha,betaa n dtheta are angles satisfying 0

if 0ltalphaltbetaltgammaltpi/ 2, then prove that tanalpha lt (sinalpha+sinbeta+singamma)/ (cosalpha+cosbeta+cosgamma)lt tangamma

If 0ltalphaltbetaltgammaltpi/2 then the equation 1/(x-sinalpha)+1/(x-sinbeta)+1/(x-singamma)=0 has (A) imaginary roots (B) real and equal roots (C) real and unequal roots (D) rational roots

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 alphagt0, betagt0, gammagt0 and alpha+beta+gamma lt pi/2 show that tanalphatanbeta+tanbetatangamma+tangammatanalphalt1

If 0 lt alpha lt beta lt gamma lt pi//2 , then the equation (x-sinbeta)(x-singamma)+(x-sinalpha)(x-singamma)+(x-sinalpha)(x-sinbeta)=0 has

If alphagt0, betagt0, gammagt0, alpha+beta+gamma= pi show that sin^2alpha+sin^2beta-sin^2gamma =

By geometrical interpretation, prove that (i) sin(alpha+beta)=sin alpha cos beta+sinbeta cosalpha (ii) cos(alpha+beta)=cosalpha cosbeta -sin alpha sinbeta

If alpha,beta,gamma, in (0,pi/2) , then prove that (s i(alpha+beta+gamma))/(sinalpha+sinbeta+singamma)<1

If tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha) then show that sinalpha+cosalpha=sqrt(2)costheta .