If `cosalpha+cosbeta=1/2a n dsinalpha+sinbeta=1/3,t h e n`

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

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

If sinalpha-sinbeta=1/3andcosbeta-cosalpha=1/2, show that cot(alpha+beta)/2=2/3

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

Statement 1: If cosalpha,cosbeta,a n dcosgamma are the direction cosines of any line segment, then cos^2alpha+cos^2beta+cos^2gamma=1. Statement 2: If cosalpha,cosbeta,a n dcosgamma are the direction cosines of any line segment, then cos2alpha+cos2beta+cos2gamma=1.

vec A isa vector with direction cosines cosalpha,cosbetaa n dcosgammadot Assuming the y-z plane as a mirror, the directin cosines of the reflected image of vec A in the plane are a. cosalpha,cosbeta,cosgamma b. cosalpha,-cosbeta,cosgamma c. -cosalpha,cosbeta,cosgamma d. -cosalpha,-cosbeta,-cosgamma

vec A isa vector with direction cosines cosalpha,cosbetaa n dcosgammadot Assuming the y-z plane as a mirror, the directin cosines of the reflected image of vec A in the plane are a. cosalpha,cosbeta,cosgamma b. cosalpha,-cosbeta,cosgamma c. -cosalpha,cosbeta,cosgamma d. -cosalpha,-cosbeta,-cosgamma

If cosalpha=1/2(x+1/x)a n dcosbeta=1/2(y+1/y),(x y >0); x , y ,alpha,beta in R then sin(alpha+beta+gamma+singammaAAgamma in R cosalphacosbeta=1AAalpha,beta in R (cosalpha+cosbeta)^2=4AAalpha,beta in R sin(alpha+beta+gamma)=sinalpha+sinbeta+s ingammaAAa , b ,gamma in R