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If sintheta+sinvarphi=a and costhetavar...

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`

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