If `cosalpha/cosbeta=m` and `cosalpha/sinbeta=n` then Show that `(m^2+n^2) cos^2beta=n^2` .

If cot theta+cos theta=m, cot theta-cos theta=n , show that : (m^2-n^2)^2=16mn .

If tantheta+sintheta=m,tantheta-sintheta=n , then show that m^2-n^2=4sqrt(mn) .

If sinalpha+sinbeta=a and cosalpha+cosbeta=b , prove that tan(alpha-beta)/2=+-sqrt((4-a^2-b^2)/(a^2+b^2)) .

If xcosalpha+ysinalpha=xcosbeta+ysinbeta=2a then cosalpha cosbeta=

If m^2+m'^2+ 2mm' cos theta =1, n^2+n'^2+2 n n' cos theta =1 and mn+m'n’ +(mn’ +m’n) cos theta=0 , prove that m^2+ n^2= cosec^2 theta .

If cosalpha+cosbeta+cosgamma=0=sinalpha+sinbeta+singamma , then which of the following is/are true:- (a) cos(alpha-beta)+cos(beta-gamma)+cos(gamma-delta)=-3/2 (b) cos(alpha-beta)+cos(beta-gamma)+cos(gamma-delta)=-1/2 (c) sumcos2alpha+2cos(alpha+beta)+2cos(beta+gamma)+2cos(gamma+alpha)=0 (d) sumsin2alpha+2sin(alpha+beta)+2sin(beta+gamma)+2sin(gamma+alpha)=0

If tan alpha= n tan beta and sin alpha= m sin beta , prove that cos^2 alpha= (m^2-1)/(n^2-1) .

Evaluate |[cosalphacosbeta,cosalphasinbeta,-sinalpha],[-sinbeta,cosbeta,0],[sinalphcosbeta,sinalphasinbeta,cosalpha]|

If sin alpha+sinbeta=l, cos alpha+ cos beta= m and tan(alpha/2)tan(beta/2)=n(!= 1) , then

Prove that cosalpha+cosbeta+cosgamma+cos(alpha+beta+gamma)=4cos(alpha+beta)/(2)cos(beta+gamma)/2cos(gamma+alpha)/2