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

If sinx-siny=a and cosx+cosy=b,prove that tan((x+y)/2)=+-sqrt((4-a^2-b^2)/(a^2+b^2))

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

If cosalpha+cosbeta=1/3 and sinalpha+sinbeta=1/4 ,show that tan ((alpha+beta)/2)=3/4

If sinalpha+sinbeta=1/2 , cosalpha+cosbeta=5/4 find the value of tanalpha+tanbeta

If cos alpha+ cos beta= a sin alpha+ sin beta=b , then show that "tan" (alpha)/(2)+"tan" (beta)/(2)= (4b)/(a^(2)+b^(2)+2a)

If tan(alpha+beta)=a+b and tan(alpha-beta)=a-b then show that atanalpha-btanbeta=a^2-b^2

If angles alpha and beta satisfy the equation a cos theta+ b sin theta= c(a,b,c are constants), prove that- (a) sin (alpha+ beta)= (2ab)/(a^(2)+b^(2)) (b) cos (alpha+beta)=(a^(2)-b^(2))/(a^(2)+b^(2)) (c) cos (alpha- beta)=(2c^(2)-(a^(2)+b^(2)))/(a^(2)+b^(2))

If cosalpha+cosbeta=2/3 and sinalpha+sinbeta=2/5 then find the vvalue of tan((alpha+beta)/2)

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 " "cos alpha+cosbeta=1/3 " and " sinalpha+sin beta=1/4, "show that" " tan"(alpha+beta)/2=3/4