If `sintheta+sinvarphi=a` and `costhetavarphi+cosvarphi=b` , then `cos((theta-varphi)/2)=+-1/2sqrt(a^2+b^2)` `cos((theta-varphi)/2)=+-sqrt(a^2-b^2)` `tan((theta-varphi)/2)=+-sqrt((4-a^2-b^2)/(a^2+b^2))` `cos(theta-varphi)=(a^2+b^2-2)/2`

If sin theta+sin varphi=a and cos theta varphi+cos varphi=b then cos((theta-varphi)/(2))=+-(1)/(2)sqrt(a^(2)+b^(2))cos((theta-varphi)/(2))=+-sqrt(a^(2)-b^(2))tan((theta-varphi)/(2))=+-sqrt((4-a^(2)-b^(2))/(a^(2)+b^(2)))cos(theta-varphi)=(a^(2)+b^(2)-2)/(2)

If sin theta +sin phi=a and cos theta +cos phi =b then prove cos (theta +phi)=(b^(2)-a^(2))/(b^(2)+a^(2))

If quad 2 theta+s in2 varphi=(1)/(2) and cos2 theta+cos2 varphi=(3)/(2), then cos^(2)(theta-varphi)=3/8b.5/8c.3/4d5/4

tan theta.tan phi=sqrt((a-b)/(a+b)), then (a-b cos2 theta)(a-b cos2 phi)=

sin theta + sin phi = a, cos theta + cos phi = b then prove tan [(theta-phi) / (2)] = + - sqrt ((4-a ^ (2) -b ^ (2)) / (a ^ (2) + b ^ (2)))

If 3 tan theta tan phi=1 , then prove that 2 cos (theta+varphi)=cos (theta-varphi) .

Prove that: (sin(theta+varphi)-2sin theta+sin(theta-varphi))/(cos(theta+varphi)-2cos theta+cos(theta-varphi))=tan theta

(tan(theta+varphi)+tan(theta-varphi))/(1-tan(theta+varphi)tan(theta-varphi))=tan2 theta

If tan theta.tan phi = sqrt ((a -b)/(a +b)), then (a -b cos 2 theta)(a -b cos 2 phi) is