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

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

If cosalpha+cosbeta+cosgamma=0a n da l sosinalpha+sinbeta+singamma=0, then prove that cos2alpha+cos2beta+cos2gamma =sin2alpha+sin2beta+sin2gamma=0 sin3alpha+sin3beta+sin3gamma=3sin(alpha+beta+gamma) cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)

Prove that ((n + 1)/(2))^(n) gt n!

If a costheta+bsintheta=m and a sintheta-bcostheta=n," then Prove that " a^(2)+b^(2)=m^(2)+n,

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

If tantheta=ntanalpha and sintheta=msinalpha then prove that cos^(2)theta=(m^(2)-1)/(n^(2)-1),n!=+-1.

Prove that |cosalpha-cosbeta|lt=|alpha-beta|