tan theta/2 = 5/2 and tan phi/2 =3/4 then cos( theta + phi)=??

Dear Student,

Please find the attached solution.

Given that tanA2 = 52 and tanB2 = 34We know that tanx+y = tanx+tany1-tanxtanyso tanA2+B2 = tanA+B2 = tanA2+tanB21-tanA2tanB2                            = 52+341-52×34 = 10+348-158 = 134-78                            = -267So value of cos(A+B) = 1-tan2A+B21+tan2A+B2 = 1--26721+-2672                                         = 1+676491-67649 = 7254962749 = 725627                                         

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